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We remind the definition and main properties of the Krichever quasiclassical tau-function, and turn to the application of these formulas for recent studies of two-dimensional quantum gravity. We show, that in the case of minimal gravity it turns to be directly related with the Verlinde formula for minimal models, giving in particular case its one more direct proof. Generalizations for continuous "complex Liouville" theory are also briefly discussed. [ABSTRACT FROM AUTHOR]

The modification of Heisenberg's uncertainty principle (HUP), is considered valuable in modern theoretical physics due to its implications on quantum gravity effects. In this paper, we attempted to derive an equation of state for dark energy, using the extended uncertainty principle (EUP) which includes a defined maximum length. We then compared this novel equation with the equations of state obtained from cosmological observations. The observational constraints on dark energy equation of states and the second law of thermodynamics suggest that the EUP parameter sign with maximum length must change. [ABSTRACT FROM AUTHOR]

Holographic dark energy theories present a fascinating interface to probe late-time cosmology, as guided by contemporary ideas about quantum gravity. In this work, we present a new holographic dark energy scenario designated "Fractional Holographic Dark Energy" (FHDE). This model extends the conventional framework of HDEs by incorporating specific features from fractional calculus and fractional Wheeler-De Witt equation recently applied, e.g., in cosmological settings. In this manner, we retrieve a novel form of HDE energy density. We then show how FHDE can provide a consistent picture of the evolution of the late-time universe even with the simple choice of the Hubble horizon as the IR (infrared) cutoff. We provide detailed descriptions of the cosmological evolution, showing how the fractional calculus ingredients can alleviate quite a few issues associated with the conventional HDE scenario. Concretely, we compute and plot diagrams using the Hubble horizon cutoff for HDE. The density parameters for DE and dark matter (DM), the deceleration parameter, and the DE EoS parameter indicate how the universe may evolve within our "FHDE" model, fitting within an appropriate scenario of late-time cosmology. [ABSTRACT FROM AUTHOR]

Recently, two types of static black hole models that retain general covariance have been proposed within the Hamiltonian constraint approach to effective quantum gravity (EQG). We have studied the light rings and shadows of these black holes using the topological method and the backward ray-tracing method, respectively. We demonstrate that these light rings in both types of static black holes are standard and unstable according to the classification of light rings. Subsequently, we checked the position of the light rings using the photon trajectory equation. We found that although the quantum parameters do not affect the light rings of these two types of black holes, they do reduce the size of the first type of static black hole in EQG, making it smaller. However, for the second type of static black hole in EQG, we cannot distinguish it from a Schwarzschild black hole based on the shadow alone. Fortunately, the quantum parameters shrink the lensing rings of both types of black holes in EQG, causing the black hole shadow to occupy a larger proportion within the ring. This can serve as a basis for distinguishing whether the black hole is in EQG or general relativity (GR). [ABSTRACT FROM AUTHOR]

We introduce an innovative method to explore gravity's quantum aspects using a novel theoretical framework. Our model delves into gravity-induced entanglement (GIE) while sidestepping classical communication limitations imposed by the LOCC principle. Specifically, we connect a non-relativistic two-dimensional quantum oscillator detector with linearly polarized gravitational waves (GWs), leveraging the quantum properties inherent in GWs to observe GIE within the oscillator's quantum states. Because our model adheres to both the "event" and the "system" localities, the detected GIE serves as a robust indicator of gravity's quantum nature. Detecting this entanglement via gravitational wave detectors could corroborate gravity's quantization and unveil crucial properties of its sources. [ABSTRACT FROM AUTHOR]

We investigate the emergence of a quantum Big-Bounce in the context of an isotropic Universe, filled by a self-interacting scalar field, which plays the role of a physical clock. The bouncing cosmology is the result of a scattering process, driven by the scalar field potential, which presence breaks down the frequency separation of the Wheeler-DeWitt equation, treated in strict analogy to a relativistic quantum system. Differently from previous analyses, we consider a really perturbative self-interaction potential, affecting the dynamics in a finite range of the time labeled by the scalar clock (and in particular we remove the divergent character previously allowed). The main result of the present analysis is that, when the Relativistic Quantum Mechanics formalism is properly implemented in the Mini-superspace analogy, the probability amplitude for the bounce is, both in the standard and polymerized case, characterized by a maximum in correspondence of the quasi-classical condition of a Universe minimum volume. [ABSTRACT FROM AUTHOR]

Particle decays are always accompanied by the emission of graviton quanta of gravity through bremsstrahlung processes. However, the corresponding branching ratio is suppressed by the square of the ratio of particle's mass to the Planck scale. The resulting present abundance of gravitational waves (GWs), composed of gravitons, is analogously suppressed. We show that superheavy particles, as heavy as the Planck scale, can be naturally produced during the post-inflationary reheating stage in the early Universe and their decays yield dramatic amounts of GWs over broad frequency range. GW observations could hence directly probe Planck-scale physics, notoriously challenging to explore. [ABSTRACT FROM AUTHOR]

We discuss the interrelations between several ideas in quantum gravity – holography, the Swampland, and the concept of ensemble averaging. To do so, we study ensemble averages of Narain-type theories associated with general even quadratic forms and their holographic duals. We establish the emergence of global symmetries and discuss their consistency with conjectures forbidding such symmetries. We also discuss how the spectral decomposition of Narain partition functions suggests a natural embedding of ensemble averaging within the low-energy limit of certain string compactifications, which in turn allows a connection with the Swampland program. [ABSTRACT FROM AUTHOR]

We revisit the genuine Fayet–Iliopoulos terms of 4D N=1 supergravity. Such terms are commonly believed to preserve a global symmetry, and therefore they are in conflict with the principles of quantum gravity. However, we find that generically there do exist supersymmetric terms that break explicitly the specific global symmetry, while preserving gauge invariance. We illustrate this, by providing a series of examples, including superpotentials and superspace higher order terms, along with a general prescription for their construction. [ABSTRACT FROM AUTHOR]

Generalized uncertainty principles are effective changes to the Heisenberg uncertainty principle that emerge in several quantum gravity models. In the present letter, we study the consequences that two classes of these modifications yield on the physics of neutrinos. Besides analyzing the change in the oscillation probabilities that the generalized uncertainty principles entail, we assess their impact on the neutrino coherence length and their possible interpretation as nonstandard neutrino interactions. Constraints cast by present and planned neutrino experiments on the generalized uncertainty principles parameters are also derived. [ABSTRACT FROM AUTHOR]

Asymptotic safety is a promising mechanism for obtaining a consistent and predictive quantum theory for gravity. The ADM formalism allows to introduce a (Euclidean) time-direction in this framework. It equips spacetime with a foliation structure by encoding the gravitational degrees of freedom in a lapse function, shift vector, and a metric measuring distances on the spatial slices. We use the Wetterich equation to study the renormalization group flow of the graviton 2-point function extracted from the spatial metric. The flow is driven by the 3- and 4-point vertices generated by the foliated Einstein-Hilbert action supplemented by minimally coupled scalar and vector fields. We derive bounds on the number of matter fields cast by asymptotic safety. Moreover, we show that the phase diagram obtained in the pure gravity case is qualitatively stable within these bounds. An intriguing feature is the presence of an IR-fixed point for the graviton mass which prevents the squared mass taking negative values. This feature persists for any number of matter fields and, in particular, also in situations where there is no suitable interacting fixed point rendering the theory asymptotically safe. Our work complements earlier studies of the subject by taking contributions from the matter fields into account. [ABSTRACT FROM AUTHOR]

We investigate the quantum deformation of the Wheeler–DeWitt equation of a Schwarzchild black hole. Specifically, the quantum deformed black hole is a quantized model constructed from the quantum Heisenberg–Weyl Uq(h4) group. We show that the event horizon area and the mass are quantized, degenerate, and bounded. The degeneracy of states indicates entangled quantum black hole/white hole states. Accordingly, quantum deformation provides a new framework to examine Einstein–Rosen wormhole solutions. Besides, we obtain the mass, the temperature, and the entropy of the q-deformed quantum Schwarzschild black hole. We find an upper bound on the mass of a black hole/white hole pair. Also, at the quantum deformation level, the entropy of the black hole contains three parts: the usual Bekenstein–Hawking entropy, the logarithmic term, and a Cube of usual black hole entropy.

We test the validity of the Generalized Heisenberg's Uncertainty principle in the presence of strong gravitational fields nearby rotating black holes; Heisenberg's principle is supposed to require additional correction terms when gravity is taken into account, leading to a more general formulation also known as the Generalized Uncertainty Principle. Using as probes electromagnetic waves acquiring orbital angular momentum when lensed by a rotating black hole, we find from numerical simulations a relationship between the spectrum of the orbital angular momentum of light and the corrections needed to formulate the Generalized Uncertainty Principle, here characterized by the rescaled parameter β0, a function of the Planck's mass and the bare mass of the black hole. Then, from the analysis of the observed twisted light due to the gravitational field of the compact object observed in M87, we find new limits for the parameter β0. With this method, complementary to black hole shadow circularity analyses, we obtain more precise limits from the experimental data of M87*, confirming the validity of scenarios compatible with General Relativity, within the uncertainties due to the experimental errors present in EHT data and those due to the numerical simulations and analysis.

Theories of Quantum Gravity as well as string theory suggest the existence of a minimal measurable length and the related Generalized Uncertainty Principle (GUP). The universality of Quantum Gravity implies that the GUP influences every quantum mechanical process. Neutrino oscillation as a quantum phenomenon exhibits quantumness at macroscopic distances and could provide potentially a suitable room for quantum foundation explorations. In this paper, we perturbatively derive the neutrino oscillation probability based on the GUP and by treating neutrinos as wave packets. We see that the GUP modifications are dependent on the effective position width of the transition amplitude σ x such that with the smaller σ x we can obtain a stronger bound on the minimal length scale in comparison to what is expected from standard model interactions. More explicitly, one can obtain an upper bound about 5 × 10 25 for the deformation parameter, β 0 , with accelerator neutrino experiments such as MINOS, provided that σ x ∼ 10 − 15 m which is reasonable since the energy of these neutrinos is of the order of a few GeV. [ABSTRACT FROM AUTHOR]

Complexity will be more and more essential in high-energy physics. It is naturally extended into the very early universe. Considering the universe as a quantum chaotic system, the curvature perturbation of the scalar field is identified with the two-mode squeezed state. By solving the Schrödinger equation, one can obtain the numerical solutions of the angle parameter and squeezing parameter. The solution of the squeezing parameter mainly determines the evolution of complexity. Our numeric indicates that the complexity of the modified dispersion relation will have a non-linear pattern after the horizon exits. Meanwhile, its corresponding Lyapunov index is also larger compared with the standard case. During the inflationary period, the complexity will irregularly oscillate and its scrambling time is also shorter compared with the standard case. Since the modified dispersion relation can be dubbed as the consequences of various frameworks of quantum gravity, it could be applicable to these frameworks. Finally, one can expect the framework of quantum gravity will lead to the fruitful evolution of complexity, which guides us in distinguishing various inflationary models. [ABSTRACT FROM AUTHOR]

A quest for phenomenological footprints of quantum gravity is among the central scientific tasks in the rising era of gravitational wave astronomy. We study gravitational wave dynamics within the noncommutative geometry framework, based on a Drinfeld twist and newly proposed noncommutative Einstein equation, and obtain the leading quantum correction to Regge-Wheeler potential up to first order in the noncommutativity parameter. By calculating the quasinormal mode frequencies we show that the noncommutative Schwarzschild black hole remains stable under axial gravitational perturbations. [ABSTRACT FROM AUTHOR]

A viable approach towards Quantum Gravity is the Doubly Special Relativity (DSR) framework in which an observer-independent finite energy upper bound (or a finite smallest length scale) appears quite naturally. In this work, we have studied the thermodynamic properties of an ideal gas in a specific DSR framework, known as the Magueijo-Smolin (MS) Model. We use the fact that DSR can be considered as nonlinear representation of Lorentz Group. Subsequently, various thermodynamic parameters of ideal gas have been derived in this modified framework to compare the corresponding deviations from the usual scenario due to the presence of the invariant energy (length) scale. [ABSTRACT FROM AUTHOR]

Castellano, Ruiz, and Valenzuela recently observed a remarkable "pattern" in infinite-distance limits of moduli spaces in quantum gravity, which relates the field space variation of the mass of the lightest tower of particles to the field space variation of the species scale. In this work, we show how a version of this pattern can be proven to hold for BPS particles and strings throughout the vector multiplet moduli space of a 5d supergravity theory, even in regions where the particle masses and string tensions are substantially modified relative to their asymptotic behavior in the infinite-distance limits. This suggests that a suitably defined version of the pattern may hold not merely in the asymptotic limits of moduli space, but in the interior as well. [ABSTRACT FROM AUTHOR]

Taking into account the importance of the unified theory of quantum mechanics and gravity, and the existence of a minimal length of the order of the Planck scale, we consider a modified Schrödinger equation resulting from a generalized uncertainty principle, which finds applications from the realm of quantum information to large-scale physics, with a quantum mechanically corrected gravitational interaction proposed very recently. As the resulting equation cannot be solved by common exact approaches, we propose a Bethe ansatz approach, which will be applied and whose results we will discuss, commenting on the analogy of the present study with some other interesting physical problems. [ABSTRACT FROM AUTHOR]

The existence of a minimal length is predicted by theories of quantum gravity and it is generally accepted that this minimal length should be of the order of the Planck length and hence can be observed in high energy phenomenon. We study the implications of the presence of the minimal length on the Klein-Gordon filed with ϕ4 self-interaction. Considering the process of spontaneous symmetry breaking, the potential also includes the ϕ3 term. The consequent field equation is a fourth-order differential equation and is considered to have solitary solutions. The sech method is applied and the normalized solutions are obtained in closed forms and the energy spectrum of the solitary fields is determined. The modification parameter of the theory is estimated by the width and the energy of the obtained solitary fields.

We show that in a two-dimensional model of quantum gravity the summation over all possible wormhole configurations leads to a kind of Coleman mechanism where the cosmological constant plays no role for large universes. Observers who are unable to observe the change in topology will naturally interpret the measurements of the size of the universe as being caused by a fluctuating cosmological constant, rather than fluctuating topology of spacetime.

We propose a new thought experiment, based on present-day Quantum Information Technologies, to measure quantum gravitational effects through the Bose-Marletto-Vedral (BMV) effect [1–4] by revealing the gravitational t3 phase term, its expected relationships with low-energy quantum gravity phenomena and test the equivalence principle of general relativity. The technique here proposed promise to reveal gravitational field fluctuations from the analysis of the stochastic noise associated to an ideal output of a measurement process of a quantum system. To improve the sensitivity we propose to cumulate the effects of the gravitational field fluctuations in time on the outputs of a series of independent measurements acted on entangled states of particles, like in the building of a quantum cryptographic key, and extract from the associated time series the effect of the expected gravitational field fluctuations. In fact, an ideal quantum cryptographic key, built with the sharing of maximally entangled states of particles, is represented by a random sequence of uncorrelated symbols mathematically described by a perfect white noise, a stochastic process with zero mean and without correlation between its values taken at different times. Gravitational field perturbations, including quantum gravity fluctuations and gravitational waves, introduce additional phase terms that decohere the entangled pairs used to build the quantum cryptographic key, with the result of coloring the white noise [5,6]. We find that this setup, built with massive mesoscopic particles, can potentially reveal the t3 gravitational phase term and thus, the BMV effect.

We present an analysis of the role of the charge within the self-complete quantum gravity paradigm. By studying the classicalization of generic ultraviolet improved charged black hole solutions around the Planck scale, we showed that the charge introduces important differences with respect to the neutral case. First, there exists a family of black hole parameters fulfilling the particle-black hole condition. Second, there is no extremal particle-black hole solution but quasi extremal charged particle-black holes at the best. We showed that the Hawking emission disrupts the condition of particle-black hole. By analyzing the Schwinger pair production mechanism, the charge is quickly shed and the particle-black hole condition can ultimately be restored in a cooling down phase towards a zero temperature configuration, provided non-classical effects are taken into account.

Recently, a black hole model in loop quantum gravity has been proposed by Lewandowski, Ma, Yang and Zhang (2023) [34]. The metric tensor of the quantum black hole (QBH) is a suitably modified Schwarzschild one. In this paper, we calculate the radius of the circular null geodesic (light ring) and obtain the linear approximation of it with respect to the quantum correction parameter α : r l ≃ 3 M − α 9 M. We then assume the QBH is backlit by a large, distant plane of uniform, isotropic emission and calculate the radius of the black hole shadow and its linear approximation: r s = 3 3 M − α 6 (3 M) . We also consider the photon ring structures in the shadow when the impact parameter b of the photon approaches to a critical impact parameter b c , and obtain a formula for estimating the deflection angle, which is φ def = − 2 ω r l 2 log ⁡ (1 − b c / b) + C ˜ (b c). We also numerically plot the images of shadows and photon rings of the QBH in three different illumination models and compare them with that of a Schwarzschild black hole. It is found that we could distinguish the quantum black hole with a Schwarzschild black hole via the shadow images in certain illumination models. [ABSTRACT FROM AUTHOR]

The bound on the proton lifetime is one of a small handful of observations that constrains physics not far from the Planck scale. This calls for a calculation of the proton lifetime in quantum gravity. Here, we calculate how quantum fluctuations of the metric impact four-fermion interactions which mediate proton decay. We find that quantum gravity lowers the scaling dimension of the four-fermion interaction, suppressing proton decay and raising the proton lifetime significantly. As a special case, we analyze asymptotically safe quantum gravity, in which we discover that proton-decay-mediating four-fermion interactions are strictly zero. [ABSTRACT FROM AUTHOR]

We present a semi-rigorous justification of Bekenstein's Generalized Second Law of Thermodynamics applicable to a universe with black holes present, based on a generic quantum gravity formulation of a black hole spacetime, where the bulk Hamiltonian constraint plays a central role. Specializing to Loop Quantum Gravity, and considering the inspiral and post-ringdown stages of binary black hole merger into a remnant black hole, we show that the Generalized Second Law implies a lower bound on the non-perturbative LQG correction to the Bekenstein-Hawking area law for black hole entropy. This lower bound itself is expressed as a function of the Bekenstein-Hawking area formula for entropy. Results of the analyses of LIGO-VIRGO-KAGRA data recently performed to verify the Hawking Area Theorem for binary black hole merger are shown to be entirely consistent with this Loop Quantum Gravity-induced inequality. However, the consistency is independent of the magnitude of the LQG corrections to black hole entropy, depending only on the negative algebraic sign of the quantum correction. We argue that results of alternative quantum gravity computations of quantum black hole entropy, where the quantum entropy exceeds the Bekenstein-Hawking value, may not share this consistency. [ABSTRACT FROM AUTHOR]

In this letter, we present two new types of D-dimensional nonperturbative Generalized Uncertainty Principle (GUP) which are predicted both a minimal length uncertainty and a maximal observable momentum. Then, using these GUPs, we study the density of states for D-dimensional spherical coordinate systems in the momentum space. Also, we investigate the cosmological constant in the presence of these GUPs and finally, compare their massless type with the ones were predicted by Kempf and Pedram in Refs. [1] and [18]. Moreover, using a more general form of the higher order GUP, once again we compare the massless cosmological constants.

In this letter, we show that the dimensionless parameters in the generalized uncertainty principle (GUP) can be constrained by the gravitational wave event GW150914, which was discovered by the LIGO Scientific and Virgo Collaborations. Firstly, according to the Heisenberg uncertainty principle (HUP) and the data of gravitational wave event GW150914, we derive the standard energy–momentum dispersion relation and calculate the difference between the propagation speed of gravitons and the speed of light, i.e., Δυ. Next, using two proposals regarding the GUP, we also generalize our study to the quantum gravity case and obtain the modified speed of gravitons. Finally, based on the modified speed of gravitons and Δυ, the improved upper bounds on the GUP parameters are obtained. The results show that the upper limits of the GUP parameters β0 and α0 are 2.3×1060 and 1.8×1020.

The idea that quantum gravity effects might "leak" outside the horizon of a black hole has recently been intensively considered. In this study, we calculate the quasinormal modes as a function of the location and amplitude of a generic metric perturbation distorting to the Schwarzschild spacetime. We conclude on the possible observability of quantum metric corrections by current and future gravitational wave experiments. [ABSTRACT FROM AUTHOR]

We demonstrate that the linearized Einstein gravity in de Sitter (dS) spacetime besides the evident symmetries also possesses the additional (local) symmetry h μ ν → h μ ν + E μ ν χ , where E μ ν is a spin-two projector tensor and χ is an arbitrary constant function. We argue that an anomalous symmetry associated with this hitherto 'hidden' property of the existing physics is indeed at the origin of 'dS breaking' in linearized quantum gravity. [ABSTRACT FROM AUTHOR]

We show that deformed relativistic kinematics, expected to emerge in a flat-spacetime limit of quantum gravity, predicts different lifetimes for particles and their antiparticles. This phenomenon is a consequence of Planck-scale modifications of the action of discrete symmetries. In particular we focus on deformations of the action of CPT derived from the κ -Poincaré algebra, the most studied example of Planck-scale deformation of relativistic symmetries. Looking at lifetimes of muons and anti-muons we are able to derive an experimental bound on the deformation parameter of κ ≳ 4 × 10 14 GeV from measurements at the LHC. Such bound has the potential to reach the value of κ ≳ 2 × 10 16 GeV using measurements at the planned Future Circular Collider (FCC). [ABSTRACT FROM AUTHOR]

We explore the question why our universe is four dimensional from an asymptotically safe vantage point. We find hints that asymptotically safe quantum fluctuations of gravity can only solve the U (1) Landau-pole problem in the Standard Model in four dimensions. This could single out the observed dimensionality of the universe as the critical dimensionality of asymptotically safe interactions. [ABSTRACT FROM AUTHOR]

We explore asymptotic safety of gravity-matter systems, discovering indications for a near-perturbative nature of these systems in the ultraviolet. Our results are based on the dynamical emergence of effective universality at the asymptotically safe fixed point. Our findings support the conjecture that an asymptotically safe completion of the Standard Model with gravity could be realized in a near-perturbative setting. [ABSTRACT FROM AUTHOR]

We set up a covariant renormalisation group equation on a foliated spacetime which preserves background diffeomorphism symmetry. As a first application of the new formalism, we study the effect of quantum fluctuations in Lorentz symmetry breaking theories of quantum gravity. It is found that once a small breaking is introduced e.g. at the Planck scale, quantum fluctuations enhance this breaking at low energies. A numerical analysis shows that the magnification is of order unity for trajectories compatible with a small cosmological constant. The immediate consequence is that the stringent observational constraints on Lorentz symmetry breaking are essentially scale-independent and must be met even at the Planck scale. [ABSTRACT FROM AUTHOR]

We analyse the recent proposal of measuring a quantum gravity phenomenon in the lab by entangling two mesoscopic particles gravitationally. We give a generally covariant description of this phenomenon, where the relevant effect turns out to be a quantum superposition of proper times. We point out that if General Relativity is assumed to hold for masses at this scale, measurement of this effect would count as evidence for quantum superposition of spacetime geometries. This interpretation addresses objections appeared in the literature. We observe that the effect sheds light on the Planck mass, and argue that it is very plausibly a real effect. [ABSTRACT FROM AUTHOR]

Abstract We show that a previously proposed new mechanism to eliminate quadratic divergences for scalar masses is self-consistently compatible with corrections induced by perturbative quantum gravity, provided the theory embeds consistently into a UV completion at the Planck scale. [ABSTRACT FROM AUTHOR]

Abstract We present the quantum κ -deformation of BMS symmetry, by generalizing the lightlike κ -Poincaré Hopf algebra. On the technical level our analysis relies on the fact that the lightlike κ -deformation of Poincaré algebra is given by a twist and the lightlike deformation of any algebra containing Poincaré as a subalgebra can be done with the help of the same twisting element. We briefly comment on the physical relevance of the obtained κ -BMS Hopf algebra as a possible asymptotic symmetry of quantum gravity. [ABSTRACT FROM AUTHOR]

Abstract The refined de Sitter derivative conjecture provides constraints to potentials that are low energy effective theories of quantum gravity. It can give direct bounds on inflationary scenarios and determine whether the theory is in the Landscape or the Swampland. We consider the 'Higgs inflation' scenario taking the refined de Sitter derivative conjecture into account. Obtaining the critical lines for the potential, we find a conjecture parameter space in which the 'Higgs inflation' is to be in the Landscape. Comparing with the model independent observational bounds from recent data we find that the observational bounds represent the Higgs inflation can be in the Landscape. [ABSTRACT FROM AUTHOR]

In this paper, we investigate behavior of massive and massless scalar particle around a static spherically symmetric charged black hole—so called Reissner-Nordström black hole in 3+1 dimension. We successfully discover a novel exact analytical quasibound states' wave functions and energy levels by solving the covariant Klein-Gordon wave equation. The quasibound state has complex-valued energy E = E R + i E I where the real part E R can be interpreted as the scalar particle's energy while the imaginary part represents the decay. We also discuss the Hawking radiation from the apparent horizon of Reissner-Nordström black hole which can be calculated using the scalar particle's wave function. In principle, this study could provide the possibility for laboratory testing of effects whose nature is absolutely related with quantum effects in gravity. [ABSTRACT FROM AUTHOR]

Generalized entropy, that has been recently proposed, puts all the known and apparently different entropies like The Tsallis, the Rényi, the Barrow, the Kaniadakis, the Sharma-Mittal and the loop quantum gravity entropy within a single umbrella. However, the microscopic origin of such generalized entropy as well as its relation to thermodynamic system(s) is not clear. In the present work, we will provide a microscopic thermodynamic explanation of generalized entropy(ies) from canonical and grand-canonical ensembles. It turns out that in both the canonical and grand-canonical descriptions, the generalized entropies can be interpreted as the statistical ensemble average of a series of microscopic quantity(ies) given by various powers of (− k ln ⁡ ρ) n (with n being a positive integer and ρ symbolizes the phase space density of the respective ensemble), along with a term representing the fluctuation of Hamiltonian and number of particles of the system under consideration (in case of canonical ensemble, the fluctuation on the particle number vanishes). [ABSTRACT FROM AUTHOR]

We examine the electromagnetic radiation produced by a moving charge in the QED vacuum that behaves as a dispersive medium characterized by a geometrical structure (discreteness/granularity) that emerges from loop quantum gravity. It is shown that the radiation is driven by the refractive vacuum the charged particle travels through reproducing the profile of the Cherenkov effect. [ABSTRACT FROM AUTHOR]

The anomalous scaling of Newton's constant around the Reuter fixed point is dynamically computed using the functional flow equation approach. Specifically, we thoroughly analyze the flow of the most general conformally reduced Einstein-Hilbert action. Our findings reveal that, due to the distinctive nature of gravity, the anomalous dimension η of the Newton's constant cannot be constrained to have one single value: the ultraviolet critical manifold is characterized by a line of fixed points (g ⁎ (η) , λ ⁎ (η)) , with a discrete (infinite) set of eigenoperators associated to each fixed point. More specifically, we find three ranges of η corresponding to different properties of both fixed points and eigenoperators and, in particular, for the range η < η c ≈ 0.96 the ultraviolet critical manifolds has finite dimensionality. [ABSTRACT FROM AUTHOR]

The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In the framework of loop quantum gravity, the scalar constraint is promoted to two versions of well-defined operators in a suitable Hilbert space of the coupled system, such that the physical Hamiltonian can become some symmetric operators. By the deparametrized form, a general expression of the solutions to either of the quantum scalar constraints is obtained, and the observables on the space of solutions can be constructed. Thus, the Dirac quantization procedure can be fully carried out in loop quantum gravity by this system. [ABSTRACT FROM AUTHOR]

A new class of modified gravity theories, made possible by subtle features of the canonical formulation of general covariance, naturally allows MOND-like behavior (MOdified Newtonian Dynamics) in effective space-time solutions without introducing new fields. A detailed analysis reveals a relationship with various quantum-gravity features, in particular in canonical approaches, and shows several properties of potential observational relevance. A fundamental origin of MOND and a corresponding solution to the dark-matter problem are therefore possible and testable. [ABSTRACT FROM AUTHOR]

We consider the von Neumann entropy of a thermal mixed state in quantum systems derived from mirror curves, where the kinetic terms are exponential functions of the momentum operators. Using the mathematical results on the asymptotics of the energy eigenvalues, we compute the asymptotic entropy in high temperature limit and compare with that of the conventional models. We discuss the connections with some folklores in quantum gravity, particularly on the finiteness of entropy. [ABSTRACT FROM AUTHOR]

We present a mechanism which drives Dirac neutrino masses to tiny values along the Renormalization Group flow, starting from an asymptotically safe ultraviolet completion of the third generation of the Standard Model including quantum gravity. At the same time, the mechanism produces a mass-splitting between the neutrino and the quark sector and also generates the mass splitting between top and bottom quark. The mechanism hinges on the hypercharges of the fermions and produces a tiny neutrino Yukawa coupling, because the right-handed neutrino is sterile and does not carry hypercharge. [ABSTRACT FROM AUTHOR]

We study the expansion of the Universe using an effective Friedmann equation obtained from the dynamics of GFT (Group Field Theory) isotropic condensates. The evolution equations are classical, with quantum correction terms to the Friedmann equation given in the form of effective fluids coupled to the emergent classical background. The occurrence of a bounce, which resolves the initial spacetime singularity, is shown to be a general property of the model. A promising feature of this model is the occurrence of an era of accelerated expansion, without the need to introduce an inflaton field with an appropriately chosen potential. We discuss possible viability issues of this scenario as an alternative to inflation.

We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered as a macroscopic effective dynamical quantity. Consistency with Riemannian geometry entails the presence of a time-dependent dark energy term in the modified field equations, which can be expressed in terms of the dynamical gravitational constant. We suggest that the late-time accelerated expansion of the Universe may be ascribed to quantum fluctuations in the geometry of spacetime rather than the vacuum energy from the matter sector.

Based on a previously found general class of quantum improved exact solutions composed of non-interacting (dust) particles, we model the gravitational collapse of stars. As the modeled star collapses a closed apparent 3-horizon is generated due to the consideration of quantum effects. The effect of the subsequent emission of Hawking radiation related to this horizon is taken into consideration. Our computations lead us to argue that a total evaporation could be reached. The inferred global picture of the spacetime corresponding to gravitational collapse is devoid of both event horizons and shell-focusing singularities. As a consequence, there is no information paradox and no need of firewalls.

Abstract We propose the notion of a classical/quantum d u a l i t y in the gravitational case (it can be extended to other interactions). By this one means e x c h a n g i n g Bohm's quantum potential for the classical potential V Q ↔ V in the stationary quantum Hamilton–Jacobi equation (QHJE) so that V Q + V = − V 0 (ground state energy). Despite that the corresponding Schrödinger equations, and their solutions differ, their associated quantum Hamilton–Jacobi equation, and g r o u n d state energy remains the s a m e. This is how the classical/quantum duality is implemented. In this scenario Bohm's quantum potential (which coincides with the attractive Newtonian potential) is now correlated to a classical r e p u l s i v e gravitational potential (plus a constant). These results suggest that there might be a q u a n t u m origin to the classical r e p u l s i v e gravitational behavior (of the accelerated expansion) of the universe which is based on this notion of classical/quantum d u a l i t y. We hope that the notion of classical/quantum duality raised in this work in connection to the QHJE may cast further light into the deep interplay between gravity and quantum mechanics. [ABSTRACT FROM AUTHOR]