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87 results on '"Karim Noui"'

1. Degenerate higher-order Maxwell theories in flat space-time

Author: Aimeric Colléaux, David Langlois, and Karim Noui
Subjects: Effective Field Theories, Gauge Symmetry, Classical Theories of Gravity, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract: Abstract We consider, in Minkowski spacetime, higher-order Maxwell Lagrangians with terms quadratic in the derivatives of the field strength tensor, and study their degrees of freedom. Using a 3+1 decomposition of these Lagrangians, we extract the kinetic matrix for the components of the electric field, corresponding to second time derivatives of the gauge field. If the kinetic matrix is invertible, the theory admits five degrees of freedom, namely the usual two polarisations of a photon plus three extra degrees of freedom which are shown to be Ostrogradski ghosts. We also classify the cases where the kinetic matrix is non-invertible and, using analogous simple models, we argue that, even though the degeneracy conditions reduce the number of degrees of freedom, it does not seem possible to fully eliminate all potential Ostrogradski ghosts.
Published: 2024
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2. Classification of generalised higher-order Einstein-Maxwell Lagrangians

Author: Aimeric Colléaux, David Langlois, and Karim Noui
Subjects: Classical Theories of Gravity, Gauge Symmetry, Effective Field Theories, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract: Abstract We classify all higher-order generalised Einstein-Maxwell Lagrangians that include terms linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength tensor. Using redundancies due to the Bianchi identities, dimensionally dependent identities and boundary terms, we show that a general Lagrangian of this form can always be reduced to a linear combination of only 21 terms, with coefficients that are arbitrary functions of the two scalar invariants derived from the field strength. We give an explicit choice of basis where these 21 terms include 3 terms linear in the Riemann tensor and 18 terms quadratic in the derivatives of the field strength.
Published: 2024
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3. Minimally modified gravity fitting Planck data better than $$\Lambda $$ Λ CDM

Author: Katsuki Aoki, Antonio De Felice, Shinji Mukohyama, Karim Noui, Michele Oliosi, and Masroor C. Pookkillath
Subjects: Astrophysics, QB460-466, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract: Abstract We study the phenomenology of a class of minimally modified gravity theories called $$f(\mathcal {H})$$ f(H) theories, in which the usual general relativistic Hamiltonian constraint is replaced by a free function of it. After reviewing the construction of the theory and a consistent matter coupling, we analyze the dynamics of cosmology at the levels of both background and perturbations, and present a concrete example of the theory with a 3-parameter family of the function f. Finally, we compare this example model to Planck data as well as some later-time probes, showing that such a realization of $$f(\mathcal {H})$$ f(H) theories fits the data significantly better than the standard $$\Lambda $$ Λ CDM model, in particular by modifying gravity at intermediate redshifts, $$z\simeq 743$$ z≃743 .
Published: 2020
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4. A remarkably simple theory of 3d massive gravity

Author: Marc Geiller and Karim Noui
Subjects: Classical Theories of Gravity, Space-Time Symmetries, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract: Abstract We propose and study a new action for three-dimensional massive gravity. This action takes a very simple form when written in terms of connection and triad variables, but the connection can also be integrated out to obtain a triad formulation. The quadratic action for the perturbations around a Minkowski background reproduces the action of self-dual massive gravity, in agreement with the expectation that the theory propagates a massive graviton. We confirm this result at the non-linear level with a Hamiltonian analysis, and show that this new theory does indeed possess a single massive degree of freedom. The action depends on four coupling constants, and we identify the various massive and topological (or massless) limits in the space of parameters. This richness, along with the simplicity of the action, opens a very interesting new window onto massive gravity.
Published: 2019
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5. Deformed General Relativity and Quantum Black Holes Interior

Author: Denis Arruga, Jibril Ben Achour, and Karim Noui
Subjects: black holes, loop quantum gravity, modified gravity, Elementary particle physics, QC793-793.5
Abstract: Effective models of black holes interior have led to several proposals for regular black holes. In the so-called polymer models, based on effective deformations of the phase space of spherically symmetric general relativity in vacuum, one considers a deformed Hamiltonian constraint while keeping a non-deformed vectorial constraint, leading under some conditions to a notion of deformed covariance. In this article, we revisit and study further the question of covariance in these deformed gravity models. In particular, we propose a Lagrangian formulation for these deformed gravity models where polymer-like deformations are introduced at the level of the full theory prior to the symmetry reduction and prior to the Legendre transformation. This enables us to test whether the concept of deformed covariance found in spherically symmetric vacuum gravity can be extended to the full theory, and we show that, in the large class of models we are considering, the deformed covariance cannot be realized beyond spherical symmetry in the sense that the only deformed theory which leads to a closed constraints algebra is general relativity. Hence, we focus on the spherically symmetric sector, where there exist non-trivial deformed but closed constraints algebras. We investigate the possibility to deform the vectorial constraint as well and we prove that non-trivial deformations of the vectorial constraint with the condition that the constraints algebra remains closed do not exist. Then, we compute the most general deformed Hamiltonian constraint which admits a closed constraints algebra and thus leads to a well-defined effective theory associated with a notion of deformed covariance. Finally, we study static solutions of these effective theories and, remarkably, we solve explicitly and in full generality the corresponding modified Einstein equations, even for the effective theories which do not satisfy the closeness condition. In particular, we give the expressions of the components of the effective metric (for spherically symmetric black holes interior) in terms of the functions that govern the deformations of the theory.
Published: 2020
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6. Spin Foams and Canonical Quantization

Author: Sergei Alexandrov, Marc Geiller, and Karim Noui
Subjects: spin foam models, loop quantum gravity, canonical quantization, Mathematics, QA1-939
Abstract: This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.
Published: 2012
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7. A Lorentz-Covariant Connection for Canonical Gravity

Author: Marc Geiller, Marc Lachièze-Rey, Karim Noui, and Francesco Sardelli
Subjects: canonical gravity, first order gravity, Lorentz-invariance, second class constraints, Mathematics, QA1-939
Abstract: We construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter. To do so, we start with the phase space formulation derived from the canonical analysis of the Holst action in which the second class constraints have been solved explicitly. This allows us to avoid the use of Dirac brackets. In this context, we show that there is a ''unique'' Lorentz-covariant connection which is commutative in the sense of the Poisson bracket, and which furthermore agrees with the connection found by Alexandrov using the Dirac bracket. This result opens a new way toward the understanding of Lorentz-covariant loop quantum gravity.
Published: 2011
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8. Linear perturbations of Einstein-Gauss-Bonnet black holes

Author: David Langlois, Karim Noui, Hugo Roussille, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de Physique des 2 Infinis Irène Joliot-Curie (IJCLab), and Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
Subjects: High Energy Physics - Theory, perturbation: asymptotic behavior, velocity, Cosmology and Nongalactic Astrophysics (astro-ph.CO), dimension: 4, compactification, gravitation: model, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), coupling: scalar, Gauss-Bonnet-Lovelock-Horndeski-Palatini etc gravity theories, General Relativity and Quantum Cosmology, horizon, Gauss-Bonnet term, propagation, general relativity, perturbation: axial, modified gravity, Exact solutions, black hole: hair, black holes and black hole thermodynamics in GR and beyond, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], perturbation: linear, higher-order: 1, differential equations, Astronomy and Astrophysics, field equations, Gravitational waves in GR and beyond: theory, field theory: scalar, High Energy Physics - Theory (hep-th), gravitation: scalar tensor, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Einstein, Schroedinger equation, Lovelock, higher-dimensional, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: We study linear perturbations about non rotating black hole solutions in scalar-tensor theories, more specifically Horndeski theories. We consider two particular theories that admit known hairy black hole solutions. The first one, Einstein-scalar-Gauss-Bonnet theory, contains a Gauss-Bonnet term coupled to a scalar field, and its black hole solution is given as a perturbative expansion in a small parameter that measures the deviation from general relativity. The second one, known as 4-dimensional-Einstein-Gauss-Bonnet theory, can be seen as a compactification of higher-dimensional Lovelock theories and admits an exact black hole solution. We study both axial and polar perturbations about these solutions and write their equations of motion as a first-order (radial) system of differential equations, which enables us to study the asymptotic behaviours of the perturbations at infinity and at the horizon following an algorithm we developed recently. For the axial perturbations, we also obtain effective Schr\"odinger-like equations with explicit expressions for the potentials and the propagation speeds. We see that while the Einstein-scalar-Gauss-Bonnet solution has well-behaved perturbations, the solution of the 4-dimensional-Einstein-Gauss-Bonnet theory exhibits unusual asymptotic behaviour of its perturbations near its horizon and at infinity, which makes the definition of ingoing and outgoing modes impossible. This indicates that the dynamics of these perturbations strongly differs from the general relativity case and seems pathological., Comment: Version accepted in JCAP
Published: 2022
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9. On the effective metric of axial black hole perturbations in DHOST gravity

Author: David Langlois, Karim Noui, Hugo Roussille, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de Physique des 2 Infinis Irène Joliot-Curie (IJCLab), and Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
Subjects: High Energy Physics - Theory, metric: Schwarzschild, family, black hole: perturbation, gravitation: model, higher-order, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Gauss-Bonnet-Lovelock-Horndeski-Palatini etc gravity theories, horizon, General Relativity and Quantum Cosmology, general relativity, symmetry: rotation, perturbation: axial, modified gravity, black hole: hair, background, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Astronomy and Astrophysics, Gravitational waves in GR and beyond: theory, singularity, gravitation: scalar tensor, High Energy Physics - Theory (hep-th), space-time: static, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], symmetry: translation
Abstract: We study axial (or odd-parity) perturbations about static and spherically symmetric hairy black hole (BH) solutions in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories. We first extend to the family of DHOST theories the first-order formulation that we recently developed for Horndeski theories. Remarkably, we find that the dynamics of DHOST axial perturbations is equivalent to that of axial perturbations in general relativity (GR) evolving in a, distinct, effective metric. In the particular case of quadratic DHOST theories, this effective metric is derived from the background BH metric via a disformal transformation. We illustrate our general study with three examples of BH solutions. In some so-called stealth solutions, the effective metric is Schwarzschild with a shifted horizon. We also give an example of BH solution for which the effective metric is associated with a naked singularity., Version accepted in JCAP
Published: 2022
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10. Asymptotics of linear differential systems and application to quasinormal modes of nonrotating black holes

Author: David Langlois, Karim Noui, Hugo Roussille, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO)
Subjects: High Energy Physics - Theory, perturbation: asymptotic behavior, Cosmology and Nongalactic Astrophysics (astro-ph.CO), black hole: perturbation, higher-order, gravitation: model, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, horizon, 0103 physical sciences, general relativity, black hole: Schwarzschild, 010306 general physics, numerical calculations, black hole: asymptotic behavior, 010308 nuclear & particles physics, background, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], quasinormal mode, field equations, boundary condition, High Energy Physics - Theory (hep-th), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Schroedinger equation, spectral, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: The traditional approach to perturbations of nonrotating black holes in General Relativity uses the reformulation of the equations of motion into a radial second-order Schr\"odinger-like equation, whose asymptotic solutions are elementary. Imposing specific boundary conditions at spatial infinity and near the horizon defines, in particular, the quasi-normal modes of black holes. For more complicated equations of motion, as encountered for instance in modified gravity models with different background solutions and/or additional degrees of freedom, we present a new approach that analyses directly the first-order differential system in its original form and extracts the asymptotic behaviour of perturbations, without resorting to a second-order reformulation. As a pedagogical illustration, we apply this treatment to the perturbations of Schwarzschild black holes and then show that the standard quasi-normal modes can be obtained numerically by solving this first-order system with a spectral method. This new approach paves the way for a generic treatment of the asymptotic behaviour of black hole perturbations and the identification of quasi-normal modes in theories of modified gravity., Comment: v2: version accepted for publication in Physical Review D
Published: 2021
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11. Black hole perturbations in modified gravity

Author: David Langlois, Karim Noui, Hugo Roussille, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO)
Subjects: High Energy Physics - Theory, perturbation: asymptotic behavior, Cosmology and Nongalactic Astrophysics (astro-ph.CO), dimension: 4, black hole: perturbation, higher-order, gravitation: model, scalar tensor, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, horizon, 0103 physical sciences, hair: scalar, black hole: Schwarzschild, 010306 general physics, numerical calculations, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], quasinormal mode, effective potential, perturbation: linear, axial, High Energy Physics - Theory (hep-th), parity, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Schroedinger equation, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: We study the linear perturbations about nonrotating black holes in the context of degenerate higher-order scalar-tensor (DHOST) theories, using a systematic approach that extracts the asymptotic behaviour of perturbations (at spatial infinity and near the horizon) directly from the first-order radial differential system governing these perturbations. For axial (odd-parity) modes, this provides an alternative to the traditional approach based on a second-order Schr\"odinger-like equation with an effective potential, which we also discuss for completeness. For polar (even-parity) modes, which contain an additional degree of freedom in DHOST theories, and are thus more complex, we use a direct treatment of the four-dimensional first-order differential system (without resorting to a second order reformulation). We illustrate our study with two specific types of black hole solutions: 'stealth' Schwarzschild black holes, with a non trivial scalar hair, as well as a class of non-stealth black holes whose metric is distinct from Schwarzschild. The knowledge of the asymptotic behaviours of the perturbations enables us to compute numerically quasi-normal modes, as we show explicitly for the non-stealth solutions. Finally, the asymptotic form of the modes also signals some pathologies in the stealth and non-stealth solutions considered here., Comment: v3: version accepted for publication in Physical Review D
Published: 2021
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12. Quadratic degenerate higher-order scalar-tensor theories revisited

Author: Hugo Roussille, Karim Noui, David Langlois, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: geometry, action: Einstein-Hilbert, General relativity, gravitation: model, Scalar (mathematics), alternative theories of gravity, curvature: scalar, 01 natural sciences, unitary gauge, General Relativity and Quantum Cosmology, Quadratic equation, Lagrangian formalism, 0103 physical sciences, surface, Tensor, gravitation: action, 010306 general physics, Mathematical physics, Physics, 010308 nuclear & particles physics, Degenerate energy levels, higher-order: 2, field theory: scalar, gravitation: scalar tensor, Metric (mathematics), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Scalar field, Scalar curvature
Abstract: International audience; We present a novel and remarkably simple formulation of degenerate higher-order scalar-tensor (DHOST) theories whose Lagrangian is quadratic in the second derivatives of some scalar field. Using disformal transformations of the metric, we identify a special “frame” (or metric) for which the Lagrangian of quadratic DHOST theories reduces to the usual Einstein-Hilbert term plus a few terms that depend on simple geometric quantities characterizing the uniform scalar-field hypersurfaces. In particular, for quadratic DHOST theories in the physically interesting class Ia, the Lagrangian simply consists of the Einstein-Hilbert term plus a term proportional to the three-dimensional scalar curvature of the uniform scalar-field hypersurfaces. The classification of all quadratic DHOST theories becomes particularly transparent in this geometric reformulation, which also applies to scalar-tensor theories that are degenerate only in the unitary gauge.
Published: 2021
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13. Reconsidering the Ostrogradsky theorem: Higher-derivatives Lagrangians, Ghosts and Degeneracy

Author: Alexander Ganz, Karim Noui, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, Physics and Astronomy (miscellaneous), higher-order, Stability (learning theory), FOS: Physical sciences, Context (language use), General Relativity and Quantum Cosmology (gr-qc), derivative: high, mechanics: classical, higher-order theories, 01 natural sciences, General Relativity and Quantum Cosmology, 0103 physical sciences, propagation, Covariant transformation, 010306 general physics, Quantum, Mathematical physics, Physics, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Degenerate energy levels, Ostrogradsky ghost, stability, ghost, Hamiltonian, High Energy Physics - Theory (hep-th), degeneracy conditions, Bounded function, covariance, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Degeneracy (mathematics), Hamiltonian (control theory)
Abstract: We review the fate of the Ostrogradsky ghost in higher-order theories. We start by recalling the original Ostrogradsky theorem and illustrate, in the context of classical mechanics, how higher-derivatives Lagrangians lead to unbounded Hamiltonians and then lead to (classical and quantum) instabilities. Then, we extend the Ostrogradsky theorem to higher-derivatives theories of several dynamical variables and show the possibility to evade the Ostrogradsky instability when the Lagrangian is "degenerate", still in the context of classical mechanics. In particular, we explain why higher-derivatives Lagrangians and/or higher-derivatives Euler-Lagrange equations do not necessarily lead to the propagation of an Ostrogradsky ghost. We also study some quantum aspects and illustrate how the Ostrogradsky instability shows up at the quantum level. Finally, we generalize our analysis to the case of higher order covariant theories where, as the Hamiltonian is vanishing and thus bounded, the question of Ostrogradsky instabilities is subtler., 30 pages, 2 figures; few typos corrected
Published: 2020
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14. Minimally Modified Gravity fitting Planck data better than $\Lambda$CDM

Author: Masroor C. Pookkillath, Karim Noui, Michele Oliosi, Shinji Mukohyama, Katsuki Aoki, Antonio De Felice, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO)
Subjects: High Energy Physics - Theory, satellite: Planck, family, Physics and Astronomy (miscellaneous), perturbation, gravitation: model, redshift: dependence, General relativity, Perturbation (astronomy), lcsh:Astrophysics, Lambda, Computer Science::Digital Libraries, 01 natural sciences, Cosmology, General Relativity and Quantum Cosmology, Theoretical physics, symbols.namesake, matter: coupling, cosmological model: parameter space, lcsh:QB460-466, 0103 physical sciences, general relativity, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, Planck, 010303 astronomy & astrophysics, Engineering (miscellaneous), Physics, background, 010308 nuclear & particles physics, dark matter: relic density, constraint: Hamiltonian, Redshift, Hamiltonian constraint, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], symbols, lcsh:QC770-798, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Phenomenology (particle physics), Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: We study the phenomenology of a class of minimally modified gravity theories called $f(\mathcal{H})$ theories, in which the usual general relativistic Hamiltonian constraint is replaced by a free function of it. After reviewing the construction of the theory and a consistent matter coupling, we analyze the dynamics of cosmology at the levels of both background and perturbations, and present a concrete example of the theory with a $3$-parameter family of the function $f$. Finally, we compare this example model to Planck data as well as some later-time probes, showing that such a realization of $f(\mathcal{H})$ theories fits the data significantly better than the standard $\Lambda$CDM model, in particular by modifying gravity at intermediate redshifts, $z\simeq743$., Comment: 21 pages, 10 figures, matches with published version
Published: 2020
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15. On rotating black holes in DHOST theories

Author: Hongguang Liu, Karim Noui, Shinji Mukohyama, Hayato Motohashi, Jibril Ben Achour, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours
Subjects: High Energy Physics - Theory, black hole: rotation, geometry, causality, Geodesic, higher-order, gravitation: model, scalar tensor, Scalar (mathematics), Kerr metric, kinetic, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Ricci, spin, 01 natural sciences, symmetry: axial, General Relativity and Quantum Cosmology, Gravitation, Theoretical physics, Singularity, matter: coupling, black hole: Kerr, 0103 physical sciences, Tensor, structure, 010306 general physics, Physics, density, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Astronomy and Astrophysics, metric: Kerr, singularity, 3. Good health, field theory: scalar, Rotating black hole, High Energy Physics - Theory (hep-th), gravitation: scalar tensor, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], time dependence, Einstein, Scalar field, geodesic
Abstract: Using the disformal solution-generating method, we construct new axisymmetric solutions in Degenerate Higher Order Scalar Tensor (DHOST) theories. The method consists in first considering a "seed" known solution in DHOST theories and then performing a disformal transformation of the metric to obtain a new solution. In vacuum, the two solutions are equivalent but they become physically inequivalent when one considers coupling to matter. In that way, we "disform" the stealth Kerr black hole solution and we obtain a first analytic rotating non-stealth solution in DHOST theories, while the associated scalar field is time-dependent with a constant kinetic density. The new solution is characterized by three parameters: the mass, the spin and the disformal parameter which encodes the deviation with respect to the Kerr geometry. We explore some geometrical properties of the novel disformed Kerr geometry which is no more Ricci flat, has the same singularity as the Kerr metric, admits an ergoregion, and is asymptotically flat. Moreover, the hidden symmetry of the Kerr solution is broken, providing an example of a non-circular geometry in a higher order theory of gravity. We also discuss geodesic motions and compute its (disformed) null directions which are interesting tools to understand the causal structure of the geometry. In addition, to illustrate again the potentiality of the disformal solution-generating method, we present another axisymmetric solution for DHOST theories obtained from a disformal transformation of the generalized Kerr solution of Einstein-Scalar gravity., 21 pages, references added, matched the published version in JCAP
Published: 2020
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16. Late-time cosmological evolution in degenerate higher-order scalar-tensor models

Author: Hamza Boumaza, Karim Noui, David Langlois, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Subjects: velocity, cosmological model, General relativity, perturbation, gravitation: model, Perturbation (astronomy), alternative theories of gravity, Parameter space, 01 natural sciences, photon: velocity, Theoretical physics, General Relativity and Quantum Cosmology, Quadratic equation, 0103 physical sciences, Friedman model, 010306 general physics, dark energy, Physics, matter: nonrelativistic, 010308 nuclear & particles physics, Gravitational wave, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Degenerate energy levels, gravitational radiation, stability, field theory: scalar, Wavelength, gravitation: scalar tensor, evolution equation, Dark energy, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], gravitation: higher-order, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], dark energy: equation of state
Abstract: International audience; We study the late cosmological evolution, from the nonrelativistic matter dominated era to the dark energy era, in modified gravity models described by degenerate higher-order scalar-tensor (DHOST) theories. They represent the most general scalar-tensor theories propagating a single scalar degree of freedom and include Horndeski and beyond Horndeski theories. We provide the homogeneous evolution equations for any quadratic DHOST theory, without restricting ourselves to theories where the speed of gravitational waves coincides with that of light since the present constraints apply to wavelengths much smaller than cosmological scales. To illustrate the potential richness of the cosmological background evolution in these theories, we consider a simple family of shift-symmetric models, characterized by three parameters and compute the evolution of dark energy and of its equation of state. We also identify the regions in parameter space where the models are perturbatively stable.
Published: 2020
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17. Deformed General Relativity and Quantum Black Holes Interior

Author: Karim Noui, Jibril Ben Achour, Denis Arruga, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)
Subjects: lcsh:QC793-793.5, General relativity, Constraint algebra, gravitation: model, gravitation: deformation, FOS: Physical sciences, General Physics and Astronomy, polymer: model, General Relativity and Quantum Cosmology (gr-qc), Loop quantum gravity, constraint: algebra, 01 natural sciences, General Relativity and Quantum Cosmology, Legendre transformation, symbols.namesake, 0103 physical sciences, Effective field theory, general relativity, symmetry: rotation, 010306 general physics, modified gravity, Physics, black hole: quantum, loop quantum gravity, 010308 nuclear & particles physics, constraint: Hamiltonian, lcsh:Elementary particle physics, Covariance, black holes, Constraint (information theory), Hamiltonian constraint, Classical mechanics, covariance, black hole: model, symbols, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], phase space: deformation, Einstein equation
Abstract: Effective models of black holes interior have led to several proposals for regular black holes. In the so-called polymer models, based on effective deformations of the phase space of spherically symmetric general relativity in vacuum, one considers a deformed Hamiltonian constraint while keeping a non-deformed vectorial constraint. In this article, we revisit and study further the question of covariance in these deformed gravity models. In particular, we propose a Lagrangian formulation for these deformed gravity models where polymer-like deformations are introduced at the level of the full theory prior to the symmetry reduction and prior to the Legendre transformation. This enables us to test whether the concept of deformed covariance found in spherically symmetric vacuum gravity can be extended to the full theory, and we show that, in the large class of models we are considering, the deformed covariance can not be realized beyond spherical symmetry in the sense that the only deformed theory which leads to a closed constraints algebra is general relativity. Hence, we focus on the spherically symmetric sector, where there exist non-trivial deformed but closed constraints algebras. We investigate the possibility to deform the vectorial constraint as well and we prove that non-trivial deformations of the vectorial constraint with the condition that the constraints algebra remains closed do not exist. Then, we compute the most general deformed Hamiltonian constraint which admits a closed constraints algebra and thus leads to a well-defined effective theory associated with a notion of deformed covariance. Finally, we study homogeneous solutions of these effective theories and, remarkably, we solve explicitly and in full generality the corresponding modified Einstein equations, even for the effective theories which do not satisfy the closeness condition., 29 pages, invited contribution to special Issue: "Probing New Physics with Black holes", Matched the published version in Universe
Published: 2019
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18. Metric formulation of the simple theory of 3d massive gravity

Author: Marc Geiller, Karim Noui, Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), AstroParticule et Cosmologie (APC (UMR_7164)), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Subjects: High Energy Physics - Theory, dimension: 3, General relativity, FOS: Physical sciences, alternative theories of gravity, General Relativity and Quantum Cosmology (gr-qc), derivative: high, Lorentz covariance, invariance: Lorentz, 01 natural sciences, symmetry breaking, General Relativity and Quantum Cosmology, Theoretical physics, 0103 physical sciences, Lorentz gauge, action: nonlinear, gravitation: massive, 010306 general physics, Physics, 010308 nuclear & particles physics, graviton: massive, Graviton, Equations of motion, field equations, 16. Peace & justice, Action (physics), Nonlinear system, Massive gravity, High Energy Physics - Theory (hep-th), graviton: propagation, Metric (mathematics), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Einstein equation
Abstract: We have recently introduced a new and very simple action for three-dimensional massive gravity. This action is written in a first order formulation where the triad and the connection play a manifestly symmetric role, but where internal Lorentz gauge symmetry is broken. The absence of Lorentz invariance, which in this model is the mechanism underlying the propagation of a massive graviton, does however prevent from writing a purely metric non-linear action for the theory. Nonetheless, in this letter, we explain how to disentangle, at the non-linear level, the metric and non-metric degrees of freedom in the equations of motion. Focusing on the metric part, we show that it satisfies modified Einstein equations with higher derivative terms. As a particular case, these equations reproduce a well-studied model known as minimal massive gravity. In the general case, we obtain new metric field equations for massive gravity in three dimensions starting from the simple first order action. These field equations are consistent through a mechanism known as "third way consistency", which our theory therefore provides a new example of., 5 pages, published version
Published: 2019
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19. Minimally Modified Gravity: a Hamiltonian Construction

Author: Shinji Mukohyama, Karim Noui, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Subjects: High Energy Physics - Theory, dimension: 4, General relativity, gravitation: model, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, Gravitation, unitary gauge, symbols.namesake, phase space, 0103 physical sciences, general relativity, Mathematical physics, Physics, diffeomorphism: invariance, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], constraint: Hamiltonian, Astronomy and Astrophysics, Invariant (physics), Hamiltonian constraint, High Energy Physics - Theory (hep-th), gravitation: scalar tensor, Phase space, symbols, ADM formalism, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Diffeomorphism, Hamiltonian (quantum mechanics), gravitation: local
Abstract: Minimally modified gravity theories are modifications of general relativity with two local gravitational degrees of freedom in four dimensions. Their construction relies on the breaking of 4D diffeomorphism invariance keeping however the symmetry under 3D diffeomorphisms. Here, we construct these theories from a Hamiltonian point of view. We start with the phase space of general relativity in the ADM formalism. Then, we find the conditions that the Hamiltonian must satisfy for the theory to propagate (up to) two gravitational degrees of freedom with the assumptions that the lapse and the shift are not dynamical, and the theory remains invariant under 3D diffeomorphisms. This construction enables us to recover the well-known "cuscuton" class of scalar-tensor theories in the unitary gauge. We also exhibit a new class of interesting theories, that we dubb $f({\cal H})$ theories, where the usual Hamiltonian constraint $\cal H$ of general relativity is replaced by $f({\cal H})$ where $f$ is an arbitrary function., 20 pages
Published: 2019
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20. Perturbations of a rotating black hole in DHOST theories

Author: David Langlois, Christos Charmousis, Karim Noui, Marco Crisostomi, Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Astrophysique Interprétation Modélisation (AIM (UMR7158 / UMR_E_9005 / UM_112)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Denis Poisson (IDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Astrophysique Interprétation Modélisation (AIM (UMR_7158 / UMR_E_9005 / UM_112)), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO)
Subjects: High Energy Physics - Theory, black hole: rotation, geometry, Physics and Astronomy (miscellaneous), General relativity, Astrophysics::High Energy Astrophysical Phenomena, scalar tensor, FOS: Physical sciences, Perturbation (astronomy), General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, 0103 physical sciences, general relativity, 010306 general physics, black hole: hair, Physics, black hole: spin, 010308 nuclear & particles physics, Gravitational wave, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], perturbation: tensor, Degenerate energy levels, perturbation: linear, parametrization, perturbation: scalar, Classical mechanics, High Energy Physics - Theory (hep-th), Rotating black hole, gravitational radiation: emission, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Teukolsky equation, gravitation: higher-order
Abstract: We study linear perturbations of a rotating black hole solution that has been recently discovered in degenerate higher-order scalar-tensor (DHOST) theories. We find a parametrization which permits the explicit resolution of the scalar perturbation while the tensor perturbation is obtained as a Teukolsky equation supplemented by an effective source term. The effective source term is related to the black hole hair and can be computed exactly for any value of the black hole spin. We discuss how the perturbations of the geometry and thus the emitted gravitational waves could be modified in comparison with general relativity., Comment: 6 pages
Published: 2019
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21. Cosmological evolution in DHOST theories

Author: David Langlois, Marco Crisostomi, Karim Noui, Kazuya Koyama, Daniele A. Steer, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Astrophysique Interprétation Modélisation (AIM (UMR_7158 / UMR_E_9005 / UM_112)), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7), Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Astrophysique Interprétation Modélisation (AIM (UMR7158 / UMR_E_9005 / UM_112)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours
Subjects: High Energy Physics - Theory, Cosmology and Nongalactic Astrophysics (astro-ph.CO), perturbation, gr-qc, scalar tensor, attractor: de Sitter, Perturbation (astronomy), FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Fixed point, coupling: minimal, System of linear equations, 01 natural sciences, General Relativity and Quantum Cosmology, symbols.namesake, Theoretical physics, De Sitter universe, 0103 physical sciences, Attractor, STFC, Physics, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], hep-th, Degenerate energy levels, RCUK, Astronomy and Astrophysics, stability, ghost, High Energy Physics - Theory (hep-th), fixed point, Homogeneous, symbols, astro-ph.CO, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], ST/N000668/1, k-essence, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Lagrangian, Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: In the context of Degenerate Higher-Order Scalar-Tensor (DHOST) theories, we study cosmological solutions and their stability properties. In particular, we explicitly illustrate the crucial role of degeneracy by showing how the higher order homogeneous equations in the physical frame (where matter is minimally coupled) can be recast in a system of equations that do not involve higher order derivatives. We study the fixed points of the dynamics, finding the conditions for having a de Sitter attractor at late times. Then we consider the coupling to matter field (described for convenience by a k-essence Lagrangian) and find the conditions to avoid gradient and ghost instabilities at linear order in cosmological perturbations, extending previous work. Finally, we apply these results to a simple subclass of DHOST theories, showing that de Sitter attractor conditions, no ghost and no gradient instabilities conditions (both in the self-accelerating era and in the matter dominated era) can be compatible., 17 pages, 2 figures. V2: error corrected in the effective dark energy equation of state
Published: 2019
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22. Scalar-tensor theories and modified gravity in the wake of GW170817

Author: Ryo Saito, David Langlois, Karim Noui, Daisuke Yamauchi, AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Laboratoire de Mathématiques et Physique Théorique ( LMPT ), Université de Tours-Centre National de la Recherche Scientifique ( CNRS ), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Laboratoire de Mathématiques et Physique Théorique (LMPT), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)
Subjects: High Energy Physics - Theory, cosmological model, Cosmology and Nongalactic Astrophysics (astro-ph.CO), higher-order, gravitation: model, scalar tensor, Scalar (mathematics), FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), gamma ray: burst, gravitational radiation: direct detection, 01 natural sciences, General Relativity and Quantum Cosmology, electromagnetic field: production, photon: velocity, [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Gravitation, nonrelativistic, Theoretical physics, 0103 physical sciences, Tensor, 010306 general physics, dark energy, Physics, 010308 nuclear & particles physics, Gravitational wave, Order (ring theory), interaction: scalar, gravitational radiation detector, field theory: scalar, Classical mechanics, High Energy Physics - Theory (hep-th), screening: Vainshtein, gravitational radiation: emission, Dark energy, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Speed of light, Scalar field, Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: Theories of dark energy and modified gravity can be strongly constrained by astrophysical or cosmological observations, as illustrated by the recent observation of the gravitational wave event GW170817 and of its electromagnetic counterpart GRB 170817A, which shows that the speed of gravitational waves, $c_g$, is the same as the speed of light, within deviations of order $10^{-15}$. This observation implies very severe restrictions on scalar-tensor theories, in particular theories whose action depends on second derivatives of a scalar field. Working in the very general framework of Degenerate Higher-Order Scalar-Tensor (DHOST) theories, which encompass Horndeski and Beyond Horndeski theories, we present the DHOST theories that satisfy $c_g=c$. We then examine, for these theories, the screening mechanism that suppresses scalar interactions on small scales, namely the Vainshtein mechanism, and compute the corresponding gravitational laws for a non-relativistic spherical body. We show that it can lead to a deviation from standard gravity inside matter, parametrized by three coefficients which satisfy a consistency relation and can be constrained by present and future astrophysical observations., Comment: 5 pages; no figure; coincides with published version
Published: 2018
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23. Generalized instantaneous modes in higher-order scalar-tensor theories

Author: Karim Noui, Shinji Mukohyama, David Langlois, Anzhong Wang, Antonio De Felice, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO)
Subjects: Physics, 010308 nuclear & particles physics, General relativity, higher-order, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], scalar tensor, Scalar (mathematics), Degenerate energy levels, Equations of motion, alternative theories of gravity, stability, field equations, 01 natural sciences, Unitary state, boundary condition, field theory: scalar, unitary gauge, Quadratic equation, 0103 physical sciences, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Boundary value problem, 010306 general physics, Scalar field, Mathematical physics
Abstract: International audience; We consider higher-order, scalar-tensor theories which appear degenerate when restricted to the unitary gauge but are not degenerate in an arbitrary gauge. We dub them U-degenerate theories. We provide a full classification of theories that are either DHOST or U-degenerate and that are quadratic in second derivatives of the scalar field and discuss its extension to cubic and higher-order theories. Working with a simple example of U-degenerate theory, we find that, for configurations in which the scalar field gradient is time-like, the apparent extra mode in such a theory can be understood as a generalized instantaneous, or “shadowy” mode, which does not propagate. Appropriate boundary conditions, required by the elliptic nature of part of the equations of motion, lead to the elimination of the apparent instability associated with this extra mode.
Published: 2018
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24. A remarkably simple theory of 3d massive gravity

Author: Karim Noui, Marc Geiller, Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Institut Denis Poisson (IDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, dimension: 3, perturbation, Perturbation (astronomy), FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, topological, Theoretical physics, symbols.namesake, 0103 physical sciences, Minkowski space, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, gravitation: massive, Minkowski, 010306 general physics, Physics, Coupling constant, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Space-Time Symmetries, graviton: massive, Graviton, Hamiltonian, Massless particle, Nonlinear system, Massive gravity, High Energy Physics - Theory (hep-th), self-duality, symbols, lcsh:QC770-798, nonlinear, Hamiltonian (quantum mechanics), Classical Theories of Gravity, simplex
Abstract: We propose and study a new action for three-dimensional massive gravity. This action takes a very simple form when written in terms of connection and triad variables, but the connection can also be integrated out to obtain a triad formulation. The quadratic action for the perturbations around a Minkowski background reproduces the action of self-dual massive gravity, in agreement with the expectation that the theory propagates a massive graviton. We confirm this result at the non-linear level with a Hamiltonian analysis, and show that this new theory does indeed possess a single massive degree of freedom. The action depends on four coupling constants, and we identify the various massive and topological (or massless) limits in the space of parameters. This richness, along with the simplicity of the action, opens a very interesting new window onto massive gravity., Comment: 20+9 pages
Published: 2018
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25. Polymer Schwarzschild black hole: An effective metric

Author: Karim Noui, Hongguang Liu, J. Ben Achour, Frédéric Lamy, AstroParticule et Cosmologie (APC (UMR_7164)), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Laboratoire de Mathématiques et Physique Théorique (LMPT), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Laboratoire de Mathématiques et Physique Théorique ( LMPT ), Centre National de la Recherche Scientifique ( CNRS ) -Université de Tours, Centre de Physique Théorique - UMR 7332 ( CPT ), and Aix Marseille Université ( AMU ) -Université de Toulon ( UTLN ) -Centre National de la Recherche Scientifique ( CNRS )
Subjects: High Energy Physics - Theory, metric: Schwarzschild, black hole: static, General Physics and Astronomy, FOS: Physical sciences, Loop quantum gravity, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, horizon, correction: quantum, [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], 0103 physical sciences, Schwarzschild metric, holonomy, black hole: Schwarzschild, symmetry: rotation, 010306 general physics, Quantum, Mathematical physics, Physics, 010308 nuclear & particles physics, Holonomy, deformation, Black hole, space-time: Reissner-Nordstroem, High Energy Physics - Theory (hep-th), Phase space, Regularization (physics), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Einstein equation, Schwarzschild radius, singularity: Schwarzschild, quantum gravity: loop space
Abstract: We consider the modified Einstein equations obtained in the framework of effective spherically symmetric polymer models inspired by Loop Quantum Gravity. When one takes into account the anomaly free point-wise holonomy quantum corrections, the modification of Einstein equations is parametrized by a function $f(x)$ of one phase space variable. We solve explicitly these equations for a static interior black hole geometry and find the effective metric describing the trapped region, inside the black hole, for any $f(x)$. This general resolution allows to take into account a standard ambiguity inherent to the polymer regularization: namely the choice of the spin $j$ labelling the SU$(2)$-representation of the holonomy corrections. When $j=1/2$, the function $f(x)$ is the usual sine function used in the polymer litterature. For this simple case, the effective exterior metric remains the classical Schwarzschild's one but acquires modifications inside the hole. The interior metric describes a regular trapped region and presents strong similarities with the Reissner-Nordstr\"om metric, with a new inner horizon generated by quantum effects. We discuss the gluing of our interior solution to the exterior Schwarzschild metric and the challenge to extend the solution outside the trapped region due to covariance requirement. By starting from the anomaly free polymer regularization for inhomogeneous spherically symmetric geometry, and then reducing to the homogeneous interior problem, we provide an alternative treatment to existing polymer interior black hole models which focus directly on the interior geometry, ignoring covariance issue when introducing the polymer regularization., Comment: 6 pages
Published: 2018
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26. Beyond Lovelock gravity: Higher derivative metric theories

Author: Marco Crisostomi, C. Charmousis, David Langlois, Karim Noui, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Laboratoire de Physique Théorique d'Orsay [Orsay] ( LPT ), Université Paris-Sud - Paris 11 ( UP11 ) -Centre National de la Recherche Scientifique ( CNRS ), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Subjects: High Energy Physics - Theory, Cosmology and Nongalactic Astrophysics (astro-ph.CO), dimension: 4, gr-qc, Lorentz transformation, [ PHYS.ASTR ] Physics [physics]/Astrophysics [astro-ph], scalar tensor, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), derivative: high, 01 natural sciences, General Relativity and Quantum Cosmology, [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th], [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Gravitation, unitary gauge, symbols.namesake, Theoretical physics, High Energy Physics::Theory, effective field theory, parity: violation, 0103 physical sciences, Effective field theory, 010306 general physics, energy: low, Physics, diffeomorphism: invariance, 010308 nuclear & particles physics, Chern-Simons term, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], hep-th, Degenerate energy levels, Parity (physics), Invariant (physics), stability, field theory: scalar, chiral, High Energy Physics - Theory (hep-th), gravitation, astro-ph.CO, symbols, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Diffeomorphism, Lovelock, Einstein-Hilbert, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Scalar field, Lorentz, Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than two degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories". Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector., 22 pages, references added, published version
Published: 2018
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27. Effective Description of Higher-Order Scalar-Tensor Theories

Author: David Langlois, Karim Noui, Filippo Vernizzi, Michele Mancarella, AstroParticule et Cosmologie (APC (UMR_7164)), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Langlois, D, Mancarella, M, Noui, K, Vernizzi, F, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Institut de Physique Théorique - UMR CNRS 3681 ( IPHT ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques et Physique Théorique ( LMPT ), and Université de Tours-Centre National de la Recherche Scientifique ( CNRS )
Subjects: High Energy Physics - Theory, Cosmology and Nongalactic Astrophysics (astro-ph.CO), dispersion relation, higher-order, gravitation: model, [ PHYS.ASTR ] Physics [physics]/Astrophysics [astro-ph], scalar tensor, Scalar (mathematics), FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th], [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], unitary gauge, Theoretical physics, 0103 physical sciences, Minkowski space, Effective field theory, dark energy theory, Tensor, Minkowski, 010306 general physics, dark energy, modified gravity, Physics, 010308 nuclear & particles physics, background, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Degenerate energy levels, perturbation: linear, Astronomy and Astrophysics, Action (physics), field theory: scalar, High Energy Physics - Theory (hep-th), cosmological perturbation theory, Dark energy, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], time dependence, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Scalar field, gravitation: Horava-Lifshitz, Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called "beyond Horndeski" theories. We also discuss Lorentz-breaking models inspired by Horava gravity., Comment: References added; matches version to appear on JCAP
Published: 2017
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28. Semiclassical analysis of black holes in loop quantum gravity: Modeling Hawking radiation with volume fluctuations

Author: Karim Noui, Pierre Heidmann, Hongguang Liu, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), École normale supérieure - Lyon (ENS Lyon), Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut de Physique Théorique - UMR CNRS 3681 ( IPHT ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ), École normale supérieure - Lyon ( ENS Lyon ), Centre de Physique Théorique - UMR 7332 ( CPT ), Aix Marseille Université ( AMU ) -Université de Toulon ( UTLN ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques et Physique Théorique ( LMPT ), Université de Tours-Centre National de la Recherche Scientifique ( CNRS ), AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), École normale supérieure de Lyon (ENS de Lyon), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, and PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)
Subjects: High Energy Physics - Theory, Event horizon, Astrophysics::High Energy Astrophysical Phenomena, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), approximation: fluid, black hole: horizon, 01 natural sciences, General Relativity and Quantum Cosmology, [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th], Micro black hole, Quantum mechanics, fluctuation: quantum, 0103 physical sciences, Extremal black hole, Volume operator, symmetry: rotation, 010306 general physics, Virtual black hole, black hole: radiation, Black hole thermodynamics, Physics, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], radiation: Hawking, scale: Planck, black hole: temperature, model: semiclassical, fluid: classical, color, Black hole, High Energy Physics - Theory (hep-th), temperature: Hawking, microstate, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], quantum gravity: loop space, Hawking radiation
Abstract: We introduce the notion of fluid approximation of a quantum spherical black hole in the context of Loop Quantum Gravity. In this limit, the microstates of the black hole are intertwiners between "large" representations $s_i$ which typically scale as $s_i \sim \sqrt{a_H}$ where $a_H$ denotes the area of the horizon in Planck units. The punctures with large colors are, for the black hole horizon, similar to what are the fluid parcels for a classical fluid. We dub them puncels. Hence, in the fluid limit, the horizon is composed by puncels which are themselves interpreted as composed (in the sense of the tensor product) by a large number of more fundamental intertwiners. We study the spectrum of the euclidean volume acting on puncels and we compute its quantum fluctuations. Then, we propose an interpretation of black holes radiation based on the properties of the quantum fluctuations of the euclidean volume operator. We estimate a typical temperature of the black hole and we show that it scales as the Hawking temperature., 18 pages, 3 figures
Published: 2017
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29. Gravity as an SU(1,1) gauge theory in four dimensions

Author: Karim Noui and Hongguang Liu
Subjects: High Energy Physics - Theory, Physics, Physics and Astronomy (miscellaneous), 010308 nuclear & particles physics, Hilbert space, FOS: Physical sciences, Loop quantum gravity, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, symbols.namesake, High Energy Physics - Theory (hep-th), 0103 physical sciences, symbols, Quantum gravity, Gauge theory, Connection (algebraic framework), Quantum field theory, 010306 general physics, Mathematical physics, Gauge symmetry, Gauge fixing
Abstract: We start with the Hamiltonian formulation of the first order action of pure gravity with a full $\mathfrak{sl}(2,\mathbb C)$ internal gauge symmetry. We make a partial gauge-fixing which reduces $\mathfrak{sl}(2,\mathbb C)$ to its sub-algebra $\mathfrak{su}(1,1)$. This case corresponds to a splitting of the space-time ${\cal M}=\Sigma \times \mathbb R$ where $\Sigma$ inherits an arbitrary Lorentzian metric of signature $(-,+,+)$. Then, we find a parametrization of the phase space in terms of an $\mathfrak{su}(1,1)$ commutative connection and its associated conjugate electric field. Following the techniques of Loop Quantum Gravity, we start the quantization of the theory and we consider the kinematical Hilbert space on a given fixed graph $\Gamma$ whose edges are colored with unitary representations of $\mathfrak{su}(1,1)$. We compute the spectrum of area operators acting of the kinematical Hilbert space: we show that space-like areas have discrete spectra, in agreement with usual $\mathfrak{su}(2)$ Loop Quantum Gravity, whereas time-like areas have continuous spectra. We conclude on the possibility to make use of this formulation of gravity to construct a holographic description of black holes in the framework of Loop Quantum Gravity., Comment: 19 pages, 2 figures
Published: 2017
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30. Mimetic gravity as DHOST theories

Author: Michele Mancarella, Filippo Vernizzi, David Langlois, Karim Noui, AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Institut de Physique Théorique - UMR CNRS 3681 ( IPHT ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ), Fédération de recherche Denis Poisson ( FRDP ), Université d'Orléans ( UO ) -Centre National de la Recherche Scientifique ( CNRS ), AstroParticule et Cosmologie (APC (UMR_7164)), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Denis Poisson (IDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Langlois, D, Mancarella, M, Noui, K, Vernizzi, F, Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO)
Subjects: High Energy Physics - Theory, Modified gravity, Cosmology and Nongalactic Astrophysics (astro-ph.CO), [ PHYS.ASTR ] Physics [physics]/Astrophysics [astro-ph], FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, Cosmological perturbation theory, [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th], Theoretical physics, Quadratic equation, 0103 physical sciences, Effective field theory, dark energy, Physics, diffeomorphism: invariance, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Degenerate energy levels, perturbation: linear, mathematical methods, Astronomy and Astrophysics, stability, Symmetry (physics), Action (physics), field theory: scalar, High Energy Physics - Theory (hep-th), gravitation: scalar tensor, Dark energy theory, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Dark energy, Diffeomorphism, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], gravitation: higher-order, Scalar field, Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: We show that theories of mimetic gravity can be viewed as degenerate higher-order scalar-tensor (DHOST) theories that admit an extra local (gauge) symmetry in addition to the usual diffeomorphism invariance. We reformulate and classify mimetic theories in this perspective. Using the effective theory of dark energy, recently extended to include DHOST theories, we then investigate the linear perturbations about a homogeneous and isotropic background for all mimetic theories. We also include matter, in the form of a $k$-essence scalar field, and we derive the quadratic action for linear perturbations in this case., Comment: 22 pages, 1 figure, references added and discussion on the instability modified. Matches the version published on JCAP
Published: 2019
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31. Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order

Author: Marco Crisostomi, Jibril Ben Achour, David Langlois, Kazuya Koyama, Gianmassimo Tasinato, Karim Noui, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Center for Gravitational Physics and Geometry (CGPG), Pennsylvania State University (Penn State), Penn State System-Penn State System, Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Observatoire de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)
Subjects: High Energy Physics - Theory, Cosmology and Gravitation, Nuclear and High Energy Physics, Cosmology and Nongalactic Astrophysics (astro-ph.CO), gr-qc, Scalar (mathematics), Motion (geometry), FOS: Physical sciences, Conformal map, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, Theoretical physics, ST/N001435/1, Quadratic equation, 0103 physical sciences, Tensor, 010306 general physics, STFC, ComputingMilieux_MISCELLANEOUS, Second derivative, Physics, [PHYS]Physics [physics], 010308 nuclear & particles physics, hep-th, Degenerate energy levels, RCUK, Cosmology of Theories beyond the SM, High Energy Physics - Theory (hep-th), astro-ph.CO, ST/N000668/1, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Scalar field, Classical Theories of Gravity, ST/K00090X/1, Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: We present all scalar-tensor Lagrangians that are cubic in second derivatives of a scalar field, and that are degenerate, hence avoiding Ostrogradsky instabilities. Thanks to the existence of constraints, they propagate no more than three degrees of freedom, despite having higher order equations of motion. We also determine the viable combinations of previously identified quadratic degenerate Lagrangians and the newly established cubic ones. Finally, we study whether the new theories are connected to known scalar-tensor theories such as Horndeski and beyond Horndeski, through conformal or disformal transformations., Comment: 29 pages, published version
Published: 2016
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32. Healthy degenerate theories with higher derivatives

Author: David Langlois, Hayato Motohashi, Teruaki Suyama, Masahide Yamaguchi, Karim Noui, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de Mathématiques et Physique Théorique ( LMPT ), Université de Tours-Centre National de la Recherche Scientifique ( CNRS ), AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, Cosmology and Nongalactic Astrophysics (astro-ph.CO), [ PHYS.ASTR ] Physics [physics]/Astrophysics [astro-ph], kinetic, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), derivative: high, mechanics: classical, 01 natural sciences, Instability, General Relativity and Quantum Cosmology, [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th], [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Matrix (mathematics), symbols.namesake, 0103 physical sciences, dark energy theory, inflation, 010306 general physics, modified gravity, Mathematical physics, Inflation (cosmology), Physics, Hamiltonian formalism, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Second-order logic, Degenerate energy levels, Astronomy and Astrophysics, stability, ghost, High Energy Physics - Theory (hep-th), symbols, Dark energy, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], time dependence, Hamiltonian (quantum mechanics), Degeneracy (mathematics), [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: In the context of classical mechanics, we study the conditions under which higher-order derivative theories can evade the so-called Ostrogradsky instability. More precisely, we consider general Lagrangians with second order time derivatives, of the form $L(\ddot\phi^a,\dot\phi^a,\phi^a;\dot q^i,q^i)$ with $a = 1,\cdots, n$ and $i = 1,\cdots, m$. For $n=1$, assuming that the $q^i$'s form a nondegenerate subsystem, we confirm that the degeneracy of the kinetic matrix eliminates the Ostrogradsky instability. The degeneracy implies, in the Hamiltonian formulation of the theory, the existence of a primary constraint, which generates a secondary constraint, thus eliminating the Ostrogradsky ghost. For $n>1$, we show that, in addition to the degeneracy of the kinetic matrix, one needs to impose extra conditions to ensure the presence of a sufficient number of secondary constraints that can eliminate all the Ostrogradsky ghosts. When these conditions that ensure the disappearance of the Ostrogradsky instability are satisfied, we show that the Euler-Lagrange equations, which involve a priori higher order derivatives, can be reduced to a second order system., Comment: 26 pages; Added footnotes 3 and 4, fixed typos in Appendix B 2, matches published version in JCAP
Published: 2016
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33. Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations

Author: David Langlois, Jibril Ben Achour, Karim Noui, AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), AstroParticule et Cosmologie (APC (UMR_7164)), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Laboratoire de Mathématiques et Physique Théorique (LMPT), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: High Energy Physics - Theory, Cosmology and Nongalactic Astrophysics (astro-ph.CO), gravitation: model, higher-order, scalar tensor, [ PHYS.ASTR ] Physics [physics]/Astrophysics [astro-ph], FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th], Gravitation, Theoretical physics, Parameterized post-Newtonian formalism, Quartic function, Quantum mechanics, 0103 physical sciences, 010306 general physics, Physics, Quadratic growth, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Degenerate energy levels, Scalar theories of gravitation, stability, field theory: scalar, High Energy Physics - Theory (hep-th), gravitation: scalar tensor, gravitation, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Degeneracy (mathematics), [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Scalar field, Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: We consider all degenerate scalar-tensor theories that depend quadratically on second order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy in general ensures the absence of Ostrogradski instability, include the quartic Horndenski Lagrangian as well as its quartic extension beyond Horndeski, but also other families of Lagrangians. We study how all these theories transform under general conformal-disformal transformations and find that they can be separated into three main classes that are stable under these transformations. This leads to a complete classification modulo conformal-disformal transformations. Finally, we show that these higher order theories include mimetic gravity and some particular khronometric theories. They also contain theories that do not correspond, to our knowledge, to already studied theories, even up to field redefinitions., 22 pages; no figure
Published: 2016
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34. Combinatorial quantisation of the Euclidean torus universe

Author: Catherine Meusburger and Karim Noui
Subjects: High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, Modular invariance, Hilbert space, FOS: Physical sciences, Clifford torus, Torus, General Relativity and Quantum Cosmology (gr-qc), Mathematical Physics (math-ph), Representation theory, General Relativity and Quantum Cosmology, symbols.namesake, Unitary representation, High Energy Physics - Theory (hep-th), Quantum mechanics, symbols, Maximal torus, Gauge theory, Mathematical Physics, Mathematical physics
Abstract: We quantise the Euclidean torus universe via a combinatorial quantisation formalism based on its formulation as a Chern-Simons gauge theory and on the representation theory of the Drinfel'd double DSU(2). The resulting quantum algebra of observables is given by two commuting copies of the Heisenberg algebra, and the associated Hilbert space can be identified with the space of square integrable functions on the torus. We show that this Hilbert space carries a unitary representation of the modular group and discuss the role of modular invariance in the theory. We derive the classical limit of the theory and relate the quantum observables to the geometry of the torus universe., 47 pages, 2 eps figures, minor changes, typos corrected
Published: 2010
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35. Non-singular black holes and the limiting curvature mechanism: a Hamiltonian perspective

Author: Frédéric Lamy, Hongguang Liu, J. Ben Achour, Karim Noui, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Centre de Physique Théorique - UMR 7332 ( CPT ), Aix Marseille Université ( AMU ) -Université de Toulon ( UTLN ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques et Physique Théorique ( LMPT ), and Université de Tours-Centre National de la Recherche Scientifique ( CNRS )
Subjects: Physics, 010308 nuclear & particles physics, FOS: Physical sciences, Equations of motion, Astronomy and Astrophysics, General Relativity and Quantum Cosmology (gr-qc), Loop quantum gravity, Curvature, 01 natural sciences, General Relativity and Quantum Cosmology, [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Black hole, symbols.namesake, Classical mechanics, Singularity, Phase space, 0103 physical sciences, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], symbols, Covariant transformation, 010306 general physics, Hamiltonian (quantum mechanics)
Abstract: We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian structure of the theory. We write down the equations of motion that we solve in the regime deep inside the black hole, and we recover that the black hole has no singularity, due to the limiting curvature mechanism. Then, we study the relation between such black holes and effective polymer black holes which have been introduced in the context of loop quantum gravity. As expected, contrary to what happens in the cosmological sector, mimetic gravity with a limiting curvature fails to reproduce the usual effective dynamics of spherically symmetric loop quantum gravity which are generically not covariant. Nonetheless, we exhibit a theory in the class of extended mimetic gravity whose dynamics reproduces the general shape of the effective corrections of spherically symmetric polymer models, but in an undeformed covariant manner. These covariant effective corrections are found to be always metric dependent, i.e. within the $\bar{\mu}$-scheme, underlying the importance of this ingredient for inhomogeneous polymer models. In that respect, extended mimetic gravity can be viewed as an effective covariant theory which naturally implements a covariant notion of point wise holonomy-like corrections. The difference between the mimetic and polymer Hamiltonian formulations provides us with a guide to understand the deformation of covariance in inhomogeneous polymer models., Comment: 32 pages, 2 figures, Clarifications added to the introduction and discussion, results unchanged, version accepted for publication in JCAP
Published: 2018
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36. Black hole spectroscopy from Loop Quantum Gravity models

Author: Xiangyu Cao, Karim Noui, Alejandro Perez, Aurélien Barrau, Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics, Nuclear and High Energy Physics, Astrophysics::High Energy Astrophysical Phenomena, Immirzi parameter, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology, Black hole, Micro black hole, Binary black hole, Quantum mechanics, Extremal black hole, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Virtual black hole, Black hole thermodynamics, Hawking radiation
Abstract: Using Monte Carlo simulations, we compute the integrated emission spectra of black holes in the framework of Loop Quantum Gravity (LQG). The black hole emission rates are governed by the entropy whose value, in recent holographic loop quantum gravity models, was shown to agree at leading order with the Bekenstein-Hawking entropy. Quantum corrections depend on the Barbero-Immirzi parameter $\gamma$. Starting with black holes of initial horizon area $A \sim 10^2$ in Planck units, we present the spectra for different values of $\gamma$. Each spectrum clearly decomposes in two distinct parts: a continuous background which corresponds to the semi-classical stages of the evaporation and a series of discrete peaks which constitutes a signature of the deep quantum structure of the black hole. We show that $\gamma$ has an effect on both parts that we analyze in details. Finally, we estimate the number of black holes and the instrumental resolution required to experimentally distinguish between the considered models., Comment: 11 pages, 9 figures
Published: 2015
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37. Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

Author: David Langlois, Karim Noui, AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Laboratoire de Mathématiques et Physique Théorique ( LMPT ), Université de Tours-Centre National de la Recherche Scientifique ( CNRS ), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, and PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)
Subjects: High Energy Physics - Theory, Cosmology and Nongalactic Astrophysics (astro-ph.CO), [ PHYS.ASTR ] Physics [physics]/Astrophysics [astro-ph], scalar tensor, Scalar (mathematics), kinetic, FOS: Physical sciences, derivative: high, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, Instability, General Relativity and Quantum Cosmology, [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th], Theoretical physics, Canonical variable, Quartic function, 0103 physical sciences, 010306 general physics, Quadratic growth, Physics, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Degenerate energy levels, Astronomy and Astrophysics, stability, 16. Peace & justice, ghost, High Energy Physics - Theory (hep-th), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], time dependence, Degeneracy (mathematics), gravitation: higher-order, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Scalar field, Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering "degenerate" Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degenerate cases. We also identify new families of scalar-tensor theories with the intriguing property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian., Comment: 19 pages, no figure
Published: 2015
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38. Background independence in a nutshell: the dynamics of a tetrahedron

Author: Winston J. Fairbairn, Luisa Doplicher, Carlo Rovelli, Leonardo Modesto, Karim Noui, and Daniele Colosi
Subjects: Physics, Physics and Astronomy (miscellaneous), 010308 nuclear & particles physics, Boundary (topology), Quantum spacetime, Equilateral triangle, 01 natural sciences, Theoretical physics, Physical information, 0103 physical sciences, Euclidean geometry, Quantum system, Background independence, 010306 general physics, Computer Science::Databases, Simple (philosophy)
Abstract: We study how physical information can be extracted from a background independent quantum system. We use an extremely simple `minimalist' system that models a finite region of 3d euclidean quantum spacetime with a single equilateral tetrahedron. We show that the physical information can be expressed as a boundary amplitude. We illustrate how the notions of "evolution" in a boundary proper-time and "vacuum" can be extracted from the background independent dynamics.
Published: 2005
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39. Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy

Author: Marc Geiller, Alejandro Perez, Olivier Asin, Jibril Ben Achour, Karim Noui, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), CPT - E4 Gravité quantique, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics, High Energy Physics - Theory, Nuclear and High Energy Physics, Quantum geometry, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Degenerate energy levels, FOS: Physical sciences, Loop quantum gravity, General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology, 3. Good health, law.invention, Black hole, Unruh effect, High Energy Physics - Theory (hep-th), law, Quantum mechanics, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Ground state, Entropy (arrow of time), Bose–Einstein condensate
Abstract: We study the thermodynamical properties of black holes when described as gases of indistinguishable punctures with a chemical potential. In this picture, which arises from loop quantum gravity, the black hole microstates are defined by finite families of half-integers spins coloring the punctures, and the near-horizon energy measured by quasi-local stationary observers defines the various thermodynamical ensembles. The punctures carry excitations of quantum geometry in the form of quanta of area, and the total horizon area $a_\text{H}$ is given by the sum of these microscopic contributions. We assume here that the system satisfies the Bose-Einstein statistics, and that each microstate is degenerate with a holographic degeneracy given by $\exp\big(\lambda a_\text{H}/\ell_\text{Pl}^2\big)$ and $\lambda>0$. We analyze in detail the thermodynamical properties resulting from these inputs, and in particular compute the grand canonical entropy. We explain why the requirements that the temperature be fixed to the Unruh temperature and that the chemical potential vanishes do not specify completely the semi-classical regime of large horizon area, and classify in turn what the various regimes can be. When the degeneracy saturates the holographic bound ($\lambda=1/4$), there exists a semi-classical regime in which the subleading corrections to the entropy are logarithmic. Furthermore, this regime corresponds to a Bose-Einstein condensation, in the sense that it is dominated by punctures carrying the minimal (or ground state) spin value $1/2$., Comment: 22 pages
Published: 2014
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40. Analytical continuation of black hole entropy in Loop Quantum Gravity: Lessons from black hole thermodynamics

Author: Karim Noui, Jibril Ben Achour, AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Laboratoire de Mathématiques et Physique Théorique ( LMPT ), Université de Tours-Centre National de la Recherche Scientifique ( CNRS ), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Subjects: group: SU(2), semiclassical, dimension: 3, group: SU(1, Loop quantum gravity, black hole: horizon, 01 natural sciences, correction: quantum, [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], General Relativity and Quantum Cosmology, 0103 physical sciences, black hole: entropy, 010306 general physics, Entropy (arrow of time), Black hole thermodynamics, Mathematical physics, Physics, black hole: thermodynamics, noncompact, 010308 nuclear & particles physics, 1), Analytic continuation, Immirzi parameter, Ashtekar variables, Black hole, self-duality, gravitation: quantization, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Quantum gravity, gauge field theory, black hole: spectrum, quantum gravity: loop space
Abstract: International audience; This contribution is devoted to summarize the recent results obtained in the construction of an “analytic continuation” of Loop Quantum Gravity (LQG). By this we mean that we construct analytic continuation of physical quantities in LQG from real values of the Barbero-Immirzi pa- rameter g to the purely imaginary g = i . This should allow us to define a quantization of gravity with self dual Ashtekar variables. We first realized in [ 1 ] that this procedure, when applied to compute the entropy of a spherical black hole in LQG for g = i , allows to reproduce exactly the Bekenstein Hawking area law at the semi classical limit. The rigorous construction of the analytic continuation of spherical black hole entropy has been done in [ 2 ]. Here we start with a review of the main steps of this construction: we recall that our prescription turns out to be unique (under natural assumptions) and leads to the right semi-classical limit with its logarithmic quantum corrections. Futhermore, the discrete and g -dependent area spectrum of the black hole horizon becomes continuous and obviously g -independent. Then, we review how this analytic continuation could be interpreted in terms of the analytic continuation from the compact gauge group SU ( 2 ) to the non compact gauge group SU ( 1 ; 1 ) relying on an analysis of three dimensional quantum gravity.
Published: 2014
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41. Spectra of geometric operators in three-dimensional loop quantum gravity: From discrete to continuous

Author: Marc Geiller, Jibril Ben Achour, Chao Yu, and Karim Noui
Subjects: Physics, General Relativity and Quantum Cosmology, Nuclear and High Energy Physics, Quantum geometry, Hořava–Lifshitz gravity, Quantum mechanics, Immirzi parameter, Spin foam, Quantum gravity, Loop quantum gravity, Euclidean quantum gravity, Loop quantum cosmology, Mathematical physics
Abstract: We study and compare the spectra of geometric operators (length and area) in the quantum kinematics of two formulations of three-dimensional Lorentzian loop quantum gravity. In the $\mathrm{SU}(2)$ Ashtekar-Barbero framework, the spectra are discrete and depend on the Barbero-Immirzi parameter $\ensuremath{\gamma}$ exactly like in the four-dimensional case. However, we show that when working with the self-dual variables and imposing the reality conditions the spectra become continuous and $\ensuremath{\gamma}$ independent.
Published: 2014
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42. Near-Horizon Radiation and Self-Dual Loop Quantum Gravity

Author: Marc Geiller and Karim Noui
Subjects: Physics, Spinor, Degenerate energy levels, General Physics and Astronomy, Spin foam, FOS: Physical sciences, Loop quantum gravity, General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology, Unruh effect, Quantum mechanics, Quantum gravity, Ground state, Effective action
Abstract: We compute the near-horizon radiation of quantum black holes in the context of self-dual loop quantum gravity. For this, we first use the unitary spinor basis of $\text{SL}(2,\mathbb{C})$ to decompose states of Lorentzian spin foam models into their self-dual and anti self-dual parts, and show that the reduced density matrix obtained by tracing over one chiral component describes a thermal state at Unruh temperature. Then, we show that the analytically-continued dimension of the $\text{SU}(2)$ Chern-Simons Hilbert space, which reproduces the Bekenstein-Hawking entropy in the large spin limit in agreement with the large spin effective action, takes the form of a partition function for states thermalized at Unruh temperature, with discrete energy levels given by the near-horizon energy of Frodden-Gosh-Perez, and with a degenerate ground state which is holographic and responsible for the entropy., 6+2 pages
Published: 2014

43. Analytic Continuation of Black Hole Entropy in Loop Quantum Gravity

Author: Amaury Mouchet, Ben Achour Jibril, Karim Noui, AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, and PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)
Subjects: Physics, Nuclear and High Energy Physics, loop quantum gravity, Event horizon, Analytic continuation, Immirzi parameter, Pacs: 04.60.Pp, FOS: Physical sciences, Loop quantum gravity, General Relativity and Quantum Cosmology (gr-qc), black holes, General Relativity and Quantum Cosmology, Black hole, thermodynamics, Classical mechanics, Chern-Simons, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Virtual black hole, Black hole thermodynamics, Mathematical physics, Hawking radiation
Abstract: We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter γ. This construction deeply relies on the link between black holes and Chern-Simons theory. Technically, the key point consists in writing the number of microstates as an integral in the complex plane of a holomorphic function, and to make use of complex analysis techniques to perform the analytic continuation. Then, we study the thermodynamical properties of the corresponding system (the black hole is viewed as a gas of indistinguishable punctures) in the framework of the grand canonical ensemble where the energy is defined a la Frodden-Gosh-Perez from the point of view of an observer located close to the horizon. The semi-classical limit occurs at the Unruh temperature T U associated to this local observer. When γ = ±i, the entropy reproduces at the semi-classical limit the area law with quantum corrections. Furthermore, the quantum corrections are logarithmic provided that the chemical potential is fixed to the simple value μ = 2T U.
Published: 2014
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44. Translation invariant time-dependent massive gravity: Hamiltonian analysis

Author: Daniele A. Steer, Jihad Mourad, and Karim Noui
Subjects: Physics, High Energy Physics - Theory, Diagonal, FOS: Physical sciences, Astronomy and Astrophysics, Invariant (physics), First order, Lorentz group, symbols.namesake, Massive gravity, High Energy Physics - Theory (hep-th), Moving frame, symbols, Hamiltonian (quantum mechanics), Reference frame, Mathematical physics
Abstract: The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system., Comment: 30 pages
Published: 2014
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45. BTZ Black Hole Entropy and the Turaev-Viro model

Author: Karim Noui and Marc Geiller
Subjects: Physics, High Energy Physics - Theory, Nuclear and High Energy Physics, 010308 nuclear & particles physics, Canonical quantization, Astrophysics::High Energy Astrophysical Phenomena, FOS: Physical sciences, Spin foam, Statistical and Nonlinear Physics, Observable, General Relativity and Quantum Cosmology (gr-qc), Cosmological constant, 01 natural sciences, General Relativity and Quantum Cosmology, High Energy Physics - Theory (hep-th), 0103 physical sciences, Euclidean geometry, 010306 general physics, Entropy (arrow of time), Mathematical Physics, BTZ black hole, Mathematical physics
Abstract: We show the explicit agreement between the derivation of the Bekenstein-Hawking entropy of a Euclidean BTZ black hole from the point of view of spin foam models and canonical quantization. This is done by considering a graph observable (corresponding to the black hole horizon) in the Turaev-Viro state sum model, and then analytically continuing the resulting partition function to negative values of the cosmological constant., 22+4 pages, 3 figures
Published: 2013

46. Statistics, holography, and black hole entropy in loop quantum gravity

Author: Karim Noui, Amit Ghosh, Alejandro Perez, Saha Institute of Nuclear Physics, Government of India, Department of Atomic Energy, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), CPT - E4 Gravité quantique, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Saha Institute of Nuclear Physics (SINP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics, High Energy Physics - Theory, Nuclear and High Energy Physics, Quantum geometry, 010308 nuclear & particles physics, Event horizon, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Horizon, FOS: Physical sciences, Semiclassical physics, General Relativity and Quantum Cosmology (gr-qc), Loop quantum gravity, 01 natural sciences, General Relativity and Quantum Cosmology, Black hole, High Energy Physics - Theory (hep-th), Quantum state, Quantum mechanics, 0103 physical sciences, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], 010306 general physics, Black hole thermodynamics
Abstract: International audience; In loop quantum gravity the quantum states of a black hole horizon are produced by point-like discrete quantum geometry excitations (or {\em punctures}) labelled by spin $j$. The excitations possibly carry other internal degrees of freedom also, and the associated quantum states are eigenstates of the area $A$ operator. On the other hand, the appropriately scaled area operator $A/(8\pi\ell)$ is also the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance $\ell$ from the horizon. Thus, the local energy is entirely accounted for by the geometric operator $A$. We assume that: In a suitable vacuum state with regular energy momentum tensor at and close to the horizon the local temperature measured by stationary observers is the Unruh temperature and the degeneracy of `matter' states is exponential with the area $\exp{(\lambda A/\ell_p^2)}$---this is supported by the well established results of QFT in curved spacetimes, which do not determine $\lambda$ but asserts an exponential behaviour. The geometric excitations of the horizon (punctures) are indistinguishable. In the semiclassical limit the area of the black hole horizon is large in Planck units. It follows that: Up to quantum corrections, matter degrees of freedom saturate the holographic bound, {\em viz.} $\lambda=\frac{1}{4}$. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-Hawking entropy $S={A}/({4\ell_p^2})$. The number of horizon punctures goes like $N\propto \sqrt{A/\ell_p^2}$, i.e the number of punctures $N$ remains large in the semiclassical limit. Fluctuations of the horizon area are small while fluctuations of the area of an individual puncture are large. A precise notion of local conformal invariance of the thermal state is recovered in the $A\to\infty$ limit where the near horizon geometry becomes Rindler.
Published: 2013
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47. Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity

Author: Karim Noui, Marc Geiller, Alejandro Perez, Ernesto Frodden, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics, High Energy Physics - Theory, Nuclear and High Energy Physics, 010308 nuclear & particles physics, Entropy (statistical thermodynamics), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Horizon, Astrophysics::High Energy Astrophysical Phenomena, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Loop quantum gravity, Lambda, 01 natural sciences, General Relativity and Quantum Cosmology, High Energy Physics - Theory (hep-th), Quantum state, 0103 physical sciences, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Quantum gravity, Spin network, 010306 general physics, BTZ black hole, Mathematical physics
Abstract: We compute the statistical entropy of a BTZ black hole in the context of three-dimensional Euclidean loop quantum gravity with a cosmological constant $\Lambda$. As in the four-dimensional case, a quantum state of the black hole is characterized by a spin network state. Now however, the underlying colored graph $\Gamma$ lives in a two-dimensional spacelike surface $\Sigma$, and some of its links cross the black hole horizon, which is viewed as a circular boundary of $\Sigma$. Each link $\ell$ crossing the horizon is colored by a spin $j_\ell$ (at the kinematical level), and the length $L$ of the horizon is given by the sum $L=\sum_\ell L_\ell$ of the fundamental length contributions $L_\ell$ carried by the spins $j_\ell$ of the links $\ell$. We propose an estimation for the number $N^\text{BTZ}_\Gamma(L,\Lambda)$ of the Euclidean BTZ black hole microstates (defined on a fixed graph $\Gamma$) based on an analytic continuation from the case $\Lambda>0$ to the case $\Lambda, Comment: 14 pages. 1 figure. Paragraph added on page 7 to clarify the horizon condition
Published: 2013
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48. Testing the role of the Barbero-Immirzi parameter and the choice of connection in Loop Quantum Gravity

Author: Chao Yu, Jibril Ben Achour, Karim Noui, and Marc Geiller
Subjects: Physics, High Energy Physics - Theory, Nuclear and High Energy Physics, Immirzi parameter, Spin foam, FOS: Physical sciences, Loop quantum gravity, General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology, Hamiltonian constraint, High Energy Physics - Theory (hep-th), Quantum mechanics, Wheeler–DeWitt equation, Quantum gravity, Spin network, Canonical quantum gravity, Mathematical physics
Abstract: We study the role of the Barbero-Immirzi parameter $\gamma$ and the choice of connection in the construction of (a symmetry-reduced version of) loop quantum gravity. We start with the four-dimensional Lorentzian Holst action that we reduce to three dimensions in a way that preserves the presence of $\gamma$. In the time gauge, the phase space of the resulting three-dimensional theory mimics exactly that of the four-dimensional one. Its quantization can be performed, and on the kinematical Hilbert space spanned by SU(2) spin network states the spectra of geometric operators are discrete and $\gamma$-dependent. However, because of the three-dimensional nature of the theory, its SU(2) Ashtekar-Barbero Hamiltonian constraint can be traded for the flatness constraint of an sl(2,C) connection, and we show that this latter has to satisfy a linear simplicity-like condition analogous to the one used in the construction of spin foam models. The physically relevant solution to this constraint singles out the non-compact subgroup SU(1,1), which in turn leads to the disappearance of the Barbero-Immirzi parameter and to a continuous length spectrum, in agreement with what is expected from Lorentzian three-dimensional gravity., Comment: 36 pages
Published: 2013
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49. Spin Foams and Canonical Quantization

Author: Marc Geiller, Karim Noui, Sergei Alexandrov, Laboratoire Charles Coulomb (L2C), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), APC - THEORIE, AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Institut für theoretische Physik, Universität Hamburg (UHH)-Universität Hamburg (UHH), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Institut für theoretische Physik, Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut für theoretische Physik
Subjects: High Energy Physics - Theory, Canonical quantization, Spin foam, FOS: Physical sciences, Loop quantum gravity, General Relativity and Quantum Cosmology (gr-qc), spin foam models, 01 natural sciences, General Relativity and Quantum Cosmology, Theoretical physics, canonical quantization, 0103 physical sciences, 010306 general physics, Mathematical Physics, Spin-½, Physics, loop quantum gravity, Spacetime, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], lcsh:Mathematics, lcsh:QA1-939, Classical mechanics, High Energy Physics - Theory (hep-th), Group field theory, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Spin network, Geometry and Topology, Canonical quantum gravity, Analysis
Abstract: 88 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"; This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.
Published: 2012
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50. Non-commutative holonomies in 2 + 1 LQG and Kauffman's brackets

Author: Karim Noui, Daniele Pranzetti, Alejandro Perez, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, and PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)
Subjects: Physics, History, 010308 nuclear & particles physics, Canonical quantization, Holonomy, Hilbert space, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Lambda, 01 natural sciences, General Relativity and Quantum Cosmology, Computer Science Applications, Education, Quantization (physics), symbols.namesake, Regularization (physics), 0103 physical sciences, symbols, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Spin network, 010306 general physics, Commutative property, Mathematical physics
Abstract: We investigate the canonical quantization of 2+1 gravity with {\Lambda} > 0 in the canonical framework of LQG. A natural regularization of the constraints of 2+1 gravity can be defined in terms of the holonomies of A\pm = A \PM \surd{\Lambda}e, where the SU(2) connection A and the triad field e are the conjugated variables of the theory. As a first step towards the quantization of these constraints we study the canonical quantization of the holonomy of the connection A_{\lambda} = A + {\lambda}e acting on spin network links of the kinematical Hilbert space of LQG. We provide an explicit construction of the quantum holonomy operator, exhibiting a close relationship between the action of the quantum holonomy at a crossing and Kauffman's q-deformed crossing identity. The crucial difference is that the result is completely described in terms of standard SU(2) spin network states., Comment: 4 pages; Proceedings of Loops'11, Madrid, to appear in Journal of Physics: Conference Series (JPCS)
Published: 2012
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