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The attempt to build a bimetric universe model made by S. Hossenfelder in 2008 could not produce any confrontations with the observation because of the violation of the equivalence principle. By using this technique again, with a subsequent modification of the signs of the terms the principles of equivalence and action-reaction are both satisfied in the model. Masses of the same sign attract each other according to Newton's law, while masses of opposite signs attract each other according to anti-Newton's law. The evolution equations are established on the basis of a generalized principle of conservation of the global energy. The observational data of the acceleration of the expansion of the sector of the positive masses leads to the conclusion that the global energy of the system is negative, dominated by the energy of the negative masses, which replace both the dark matter and the dark energy. The calculation gives then an excellent agreement with the data of 700 type Ia supernovae. Numerical simulations, integrating this dominance of negative masses, give a new scheme of large scale structure formation. The negative masses, associated with a shorter Jeans time, form first a regular network of spheroidal conglomerates. Confined in the interstitial space the positive mass acquires a structure comparable to joined soap bubbles. The compression of the positive mass according to flat plates leads to a rapid rise in temperature, followed by an equally rapid radiative cooling, which is favorable to the constitution of galaxies. On the other hand, the conglomerates of negative mass behave like immense protostars with a cooling time exceeding the age of the universe and lost in this form, giving birth neither to stars and galaxies, nor to heavy atoms, for lack of fusion reactions. Life is therefore absent in this negative sector. The phenomenon of the Great Repeller is interpreted by the presence of one of these conglomerates of negative mass, geometrically invisible, which occupy the center of the great voids of the Very Large-scale Structure (VLS). The negative mass invades the space between the galaxies and exerts on them a counter pressure that confines them, while giving their rotational curves a flat firmness at the periphery. Two-dimensional (2D) numerical simulations of a galaxy confined by its negative mass environment give rise to a barred spiral lasting for thirty years and thus shed light on the nature of an essentially dissipative phenomenon, reflecting the braking of the galaxy's rotation. We construct the group associated with this new geometry, including a matter-antimatter symmetry. The existence of negative masses and energies imposes the use of an extension of the complete Poincaré group through a global charge, parity, and time reversal (CPT) symmetry. The matterantimatter symmetry is thus also present in the negative sector, which makes it possible to take advantage of Andrei Sakharov's idea and to conclude that the invisible components of the universe are constituted by the copy of our own antimatter, endowed with a negative mass. It is predicted that laboratory antimatter with negative mass will behave like ordinary matter. The theme of this T-symmetry is then projected into the quantum domain where, classically, the negative energy states, considered as non-physical, are banished and choosing an anti-linear and anti-unitary time reversal operator. We show that by choosing a linear and unitary operator the existence of negative energy states is imposed. We conjecture that this extension of quantum mechanics could allow to quantify gravitation. The model is extended in the past by developing an alternative to the inflation model, with two sets of constants and scale factors of space and time varying jointly, in such a way that the equations of physics, in both sectors, are conserved. Lorentz invariance is thus preserved and incompatibilities with observations disappear. Cosmic homogeneities in both sectors are ensured thanks to a variable speed of light regime. In such a context, if the density in the negative sector is higher, its space scale factor is smaller while the speed of light is higher. We then consider the development of gravitational instability in the two photon gases. This one is not observable inside the same sector because its length of Jeans is then identified with the horizon. On the other hand this instability, developing in the negative sector, with a weaker Jeans length, leaves a weak imprint in the positive world, which constitutes an alternative interpretation of the cosmic microwave background (CMB) fluctuations. Its analysis in this new context allows to have access to the scale factor of the negative sector and to the value of the speed of light which corresponds to it. We conclude that the distances, measured in the negative sector, are one hundred times shorter, while the speed of light is ten times higher. This reduces the duration of interstellar travels, carried out according to the geodesics of the negative sector, which would become from then on not impossible., La tentative de construction d'un modèle d'univers bimétrique faite par S. Hossenfelder en 2008 n'a pas pu produire de confrontations avec l'observation à cause de la violation du principe d'équivalence. En utilisant à nouveau cette technique, avec une modification ultérieure des signes des termes, les principes d'équivalence et d'action-réaction sont tous deux satisfaits dans le modèle. Les masses de même signe s'attirent selon la loi de Newton, tandis que les masses de signes opposés s'attirent selon la loi anti-Newton. Les équations d'évolution sont établies sur la base d'un principe généralisé de conservation de l'énergie globale. Les données observationnelles de l'accélération de l'expansion du secteur des masses positives conduisent à la conclusion que l'énergie globale du système est négative, dominée par l'énergie des masses négatives, qui remplacent à la fois la matière noire et l'énergie noire. Le calcul donne alors un excellent accord avec les données de 700 supernovae de type Ia. Les simulations numériques, intégrant cette dominance des masses négatives, donnent un nouveau schéma de formation des structures à grande échelle. Les masses négatives, associées à un temps de Jeans plus court, forment d'abord un réseau régulier de conglomérats sphéroïdaux. Confinée dans l'espace interstitiel, la masse positive acquiert une structure comparable à des bulles de savon jointes. La compression de la masse positive selon des plaques planes conduit à une élévation rapide de la température, suivie d'un refroidissement radiatif tout aussi rapide, ce qui est favorable à la constitution des galaxies. En revanche, les conglomérats de masse négative se comportent comme d'immenses proto-étoiles dont le temps de refroidissement dépasse l'âge de l'univers et se perdent sous cette forme, ne donnant naissance ni à des étoiles et galaxies, ni à des atomes lourds, faute de réactions de fusion. La vie est donc absente dans ce secteur négatif. Le phénomène du Grand Repoussoir est interprété par la présence d'un de ces conglomérats de masse négative, géométriquement invisibles, qui occupent le centre des grands vides de la Structure à Très Grande Echelle (VLS). La masse négative envahit l'espace entre les galaxies et exerce sur elles une contre-pression qui les confine, tout en donnant à leurs courbes de rotation une fermeté plate en périphérie. Des simulations numériques bidimensionnelles (2D) d'une galaxie confinée par son environnement de masse négative donnent lieu à une spirale barrée d'une durée de trente ans et éclairent ainsi la nature d'un phénomène essentiellement dissipatif, reflétant le freinage de la rotation de la galaxie. Nous construisons le groupe associé à cette nouvelle géométrie, incluant une symétrie matière-antimatière. L'existence de masses et d'énergies négatives impose l'utilisation d'une extension du groupe de Poincaré complet à travers une symétrie globale de charge, parité et retournement temporel (CPT). La symétrie matière-antimatière est donc également présente dans le secteur négatif, ce qui permet de tirer parti de l'idée d'Andrei Sakharov et de conclure que les composantes invisibles de l'univers sont constituées par la copie de notre propre antimatière, dotée d'une masse négative. Il est prévu que l'antimatière de laboratoire dotée d'une masse négative se comporte comme la matière ordinaire. Le thème de cette symétrie T est ensuite projeté dans le domaine quantique où, classiquement, on bannit les états d'énergie négative, considérés comme non-physiques, en choisissant un opérateur de retournement temporel anti-linéaire et anti-unitaire. Nous montrons qu'en choisissant un opérateur linéaire et unitaire, l'existence des états d'énergie négative est imposée. Nous conjecturons que cette extension de la mécanique quantique pourrait permettre de quantifier la gravitation. Nous étendons le modèle en développant une alternative au modèle d'inflation, avec deux ensembles de constantes et de facteurs d'échelle de l'espace et du temps variant conjointement, de telle sorte que les équations de la physique, dans les deux secteurs, soient conservées. L'invariance de Lorentz est ainsi préservée et les incompatibilités avec les observations disparaissent. Les homogénéités cosmiques dans les deux secteurs sont assurées grâce à un régime de vitesse de la lumière variable. Dans un tel contexte, si la densité dans le secteur négatif est plus élevée, son facteur d'échelle spatiale est plus petit alors que la vitesse de la lumière est plus élevée. Nous considérons ensuite le développement d'une instabilité gravitationnelle dans les gaz à deux photons. Celle-ci n'est pas observable à l'intérieur du même secteur car sa longueur de Jeans est alors identifiée à l'horizon. En revanche, cette instabilité, se développant dans le secteur négatif, avec une longueur de Jeans plus faible, laisse une faible empreinte dans le monde positif, ce qui constitue une interprétation alternative des fluctuations du fond diffus cosmologique (CMB). Son analyse dans ce nouveau contexte permet d'accéder au facteur d'échelle du secteur négatif et à la valeur de la vitesse de la lumière qui lui correspond. Nous concluons que les distances, mesurées dans le secteur négatif, sont cent fois plus courtes, alors que la vitesse de la lumière est dix fois plus élevée. La durée des voyages interstellaires s'en trouve réduite.

International audience; In a previous paper we introduced a cosmological model describing the early inflation, the intermediate decelerated expansion, and the late accelerating expansion of the universe in terms of a single barotropic fluid characterized by a quadratic equation of state. We obtained a scalar field representation of this fluid and determined the potential V(ϕ) connecting the inflaton potential in the early universe to the quintessence potential in the late universe. This scalar field has later been called the ‘vacuumon’ by other authors, in the context of the Running Vacuum model. In this paper, we study how the scalar field potential is modified by the presence of other cosmic components such as stiff matter, black-body radiation, baryonic matter, and dark matter. We also determine the mass m and the self-interaction constant λ of the scalar field given by the second and fourth derivatives of the potential at its extrema. We find that its mass is imaginary in the early universe with a modulus of the order of the Planck mass MP=(ℏc/G)1/2=1.22×1019GeV/c2 and real in the late universe with a value of the order of the cosmon mass mΛ=(Λℏ2/c4)1/2=2.08×10−33eV/c2 predicted by string theory. Although our model is able to describe the evolution of the homogeneous background for all times, it cannot account for the spectrum of fluctuations in the early universe. Indeed, by applying the Hamilton–Jacobi formalism to our model of early inflation, we find that the Hubble hierarchy parameters and the spectral indices lead to severe discrepancies with the observations. This suggests that the vacuumon potential is just an effective classical potential that cannot be directly used to compute the fluctuations in the early universe. A fully quantum field theory may be required to achieve that goal. Finally, we discuss the connection between our model based on a quadratic equation of state and the Running Vacuum model which assumes a variation of the cosmological constant with the Hubble parameter.

In a previous paper (Chavanis, 2015) we have introduced a new cosmological model that we called the logotropic model. This model involves a fundamental constant Λ which is the counterpart of Einstein’s cosmological constant in the Λ CDM model. The logotropic model is able to account, without free parameter, for the constant surface density of the dark matter halos, for their mass–radius relation, and for the Tully–Fisher relation. In this paper, we explore other consequences of this model. By advocating a form of “strong cosmic coincidence” we predict that the present proportion of dark energy in the Universe is Ω de,0 = e ∕ ( 1 + e ) ≃ 0 . 731 which is close to the observed value. We also remark that the surface density of dark matter halos and the surface density of the Universe are of the same order as the surface density of the electron. This makes a curious connection between cosmological and atomic scales. Using these coincidences, we can relate the Hubble constant, the electron mass and the electron charge to the cosmological constant. We also suggest that the famous numbers 137 (fine-structure constant) and 123 (logotropic constant) may actually represent the same thing. This could unify microphysics and cosmophysics. We study the thermodynamics of the logotropic model and find a connection with the Bekenstein–Hawking entropy of black holes if we assume that the logotropic dark fluid is made of particles of mass m Λ ∼ ħ Λ ∕ c 2 = 2 . 08 × 1 0 − 33 eV∕c 2 (cosmons). In that case, the universality of the surface density of the dark matter halos may be related to a form of holographic principle (the fact that their entropy scales like their area). We use similar arguments to explain why the surface density of the electron and the surface density of the Universe are of the same order and justify the empirical Weinberg relation. Finally, we combine the results of our approach with the quantum Jeans instability theory to predict the order of magnitude of the mass of ultralight axions m ∼ 1 0 − 23 eV∕c 2 in the Bose–Einstein condensate dark matter paradigm.

A phase space is built that allows to study, classify and compare easily large classes of static spherically symmetric wormholes solutions, sustained by an isotropic perfect fluid in General Relativity. We determine the possible locations of equilibrium points, throats and curvature singularities in this phase space. Throats locations show that the spatial variation of the gravitational redshift at the throat of a static spherically symmetric wormhole sustained by an isotropic perfect fluid is always diverging, generalising the result that there is no such wormhole with zero-tidal force. Several specific static spherically symmetric wormholes models are studied. A vanishing density model leads to an exact solution of the field equation allowing to test our dynamical system formalism. It also shows how to extend it to the description of static black holes. Hence, the trajectory of the Schwarzschild black hole is determined. The static spherically symmetric wormhole solutions of several usual isotropic dark energy (generalised Chaplygin gas, constant, linear and Chevallier-Polarski-Linder equations of state) and dark matter (Navarro-Frenk-White profile) models are considered. They show various behaviours far from the throat: singularities, spatial flatness, cyclic behaviours, etc. None of them is asymptotically Minkowski flat. This discards the natural formation of static spherically symmetric and isotropic wormholes from these dark fluids. Last we consider a toy model of an asymptotically Minkowski flat wormhole that is a counterexample to a recent theorem claiming that a static wormhole sustained by an isotropic fluid cannot be asymptotically flat on both sides of its throat., 21 pages, 17 figures

International audience; We develop a model of Bose-Einstein condensate dark matter halos with a solitonic core and an isothermal atmosphere based on a generalized Gross-Pitaevskii equation [P. H. Chavanis, Eur. Phys. J. Plus 132, 248 (2017)EPJPA32190-544410.1140/epjp/i2017-11544-3]. This equation provides a heuristic coarse-grained parametrization of the ordinary Gross-Pitaevskii equation accounting for violent relaxation and gravitational cooling. It involves a cubic nonlinearity taking into account the self-interaction of the bosons, a logarithmic nonlinearity associated with an effective temperature, and a source of dissipation. It leads to superfluid dark matter halos with a core-halo structure. The quantum potential or the self-interaction of the bosons generates a solitonic core that solves the cusp problem of the cold dark matter model. The logarithmic nonlinearity generates an isothermal atmosphere accounting for the flat rotation curves of the galaxies. The dissipation ensures that the system relaxes towards an equilibrium configuration. In the Thomas-Fermi approximation, a dark matter halo is equivalent to a barotropic gas with an equation of state P=2πasℏ2ρ2/m3+ρkBT/m, where as is the scattering length of the bosons and m is their individual mass. We numerically solve the equation of hydrostatic equilibrium and determine the density profiles and rotation curves of dark matter halos. We impose that the surface density of the halos has the universal value Σ0=ρ0rh=141 M⊙/pc2 obtained from the observations. For a boson with ratio as/m3=3.28×103 fm/(eV/c2)3, we find a minimum halo mass (Mh)min=1.86×108 M⊙ and a minimum halo radius (rh)min=788 pc. This ultracompact halo corresponds to a pure soliton which is the ground state of the Gross-Pitaevskii-Poisson equation. For (Mh)min(Mh)* we find two branches of solutions corresponding to (i) purely isothermal halos without soliton and (ii) isothermal halos harboring a central soliton. The purely isothermal halos (gaseous phase) are stable. For Mh>(Mh)c=6.86×1010 M⊙, they are indistinguishable from the observational Burkert profile. For (Mh)*1012 M⊙ may undergo a gravothermal catastrophe leading ultimately to the formation of a supermassive black hole (for smaller halos, the gravothermal catastrophe is inhibited by quantum effects). We relate the bifurcation point and the point above which supermassive black holes may form to the canonical and microcanonical critical points (Mh)CCP=3.27×109 M⊙ and (Mh)MCP∼2×1012 M⊙ of the “thermal” self-gravitating bosonic gas. Our model has no free parameter so it is completely predictive. Extension of this model to noninteracting bosons and fermions will be presented in forthcoming papers.

International audience; We study the gravitational instability of a general relativistic complex scalar field with a quartic self-interaction in an infinite homogeneous static background. This quantum relativistic Jeans problem provides a simplified framework to study the formation of the large-scale structures of the Universe in the case where dark matter is made of a scalar field. The scalar field may represent the wave function of a relativistic self-gravitating Bose-Einstein condensate. Exact analytical expressions for the dispersion relation and Jeans length λJ are obtained from a hydrodynamical representation of the Klein-Gordon-Einstein equations [A. Suárez and P.-H. Chavanis, Phys. Rev. D 92, 023510 (2015)PRVDAQ1550-799810.1103/PhysRevD.92.023510]. We compare our results with those previously obtained with a simplified relativistic model [M. Yu. Khlopov, B. A. Malomed, and Y. B. Zeldovich, Mon. Not. R. Astron. Soc. 215, 575 (1985)MNRAA40035-871110.1093/mnras/215.4.575]. When relativistic effects are fully accounted for, we find that the perturbations are stabilized at very large scales of the order of the Hubble length λH. Numerical applications are made for ultralight bosons without self-interaction (fuzzy dark matter), for bosons with a repulsive self-interaction, and for bosons with an attractive self-interaction (QCD axions and ultralight axions). We show that the Jeans instability is inhibited in the ultrarelativistic regime of the scalar field (early Universe and radiationlike era) because the Jeans length is of the order of the Hubble length (λJ∼λH), except when the self-interaction of the bosons is attractive. By contrast, structure formation can take place in the nonrelativistic regime of the scalar field (matterlike era) for λJ≤λ≤λH. Since the scalar field has a nonzero Jeans length due to its quantum nature (Heisenberg uncertainty principle or quantum pressure due to the self-interaction of the bosons), it appears that the wave properties of the scalar field can stabilize gravitational collapse at small scales, providing halo cores and suppressing small-scale linear power. This may solve the CDM crisis such as the cusp problem and the missing satellite problem. We also compare our results with those obtained in the case where dark matter is made of fermions instead of bosons.

Relativistic location systems that extend relativistic positioning systems show that pseudo-Riemannian space-time geometry is somehow encompassed in a particular four-dimensional projective geometry. The resulting geometric structure is then that of a generalized Cartan space (also called Cartan connection space) with projective connection. The result is that locally non-linear actions of projective groups via homographies systematically induce the existence of a particular space-time foliation independent of any space-time dynamics or solutions of Einstein&rsquo, s equations for example. In this article, we present the consequences of these projective group actions and this foliation. In particular, it is shown that the particular geometric structure due to this foliation is similar from a certain point of view to that of a black hole but not necessarily based on the existence of singularities. We also present a modified Newton&rsquo, s laws invariant with respect to the homographic transformations induced by this projective geometry. Consequences on galactic dynamics are discussed and fits of galactic rotational velocity curves based on these modifications which are independent of any Modified Newtonian Dynamics (MOND) or dark matter theories are presented.

Published 3 August 2018 in the "Galaxies" journal (http://www.mdpi.com/journal/galaxies), Vol.6, Iss. 3 (Sept. 2018).; International audience; Relativistic location systems that extend relativistic positioning systems show that pseudo-Riemannian space-time geometry is somehow encompassed in a particular four-dimensional projective geometry. The resulting geometric structure is then that of a generalized Cartan space (also called Cartan connection space) with projective connection. The result is that locally non-linear actions of projective groups via homographies systematically induce the existence of a particular space-time foliation independent of any space-time dynamics or solutions of Einstein's equations for example. In this article, we present the consequences of these projective group actions and this foliation. In particular, it is shown that the particular geometric structure due to this foliation is similar from a certain point of view to that of a black hole but not necessarily based on the existence of singularities. We also present modified Newton's laws invariant with respect to the homographic transformations induced by this projective geometry. Consequences on galactic dynamics are discussed and fits of galactic rotational velocity curves based on these modificationswhich are independent of any MOND or dark matter theories are presented.

International audience; We study the nature of phase transitions between dilute and dense axion stars interpreted as self-gravitating Bose-Einstein condensates. We develop a Newtonian model based on the Gross-Pitaevskii-Poisson equations for a complex scalar field with a self-interaction potential V(|ψ|2) involving an attractive |ψ|4 term and a repulsive |ψ|6 term. Using a Gaussian Ansatz for the wave function, we analytically obtain the mass-radius relation of dilute and dense axion stars for arbitrary values of the self-interaction parameter λ≤0. We show the existence of a critical point |λ|c∼(m/MP)2, where m is the axion mass and MP is the Planck mass, above which a first-order phase transition takes place. We qualitatively estimate general relativistic corrections on the mass-radius relation of axion stars. For weak self-interactions |λ||λ|c, a system of self-gravitating axions forms a stable dilute axion star below a Newtonian maximum mass Mmax,Ndilute=5.073MP/|λ| [Phys. Rev. D 84, 043531 (2011)PRVDAQ1550-799810.1103/PhysRevD.84.043531], collapses into a dense axion star above that mass, and collapses into a black hole above a general relativistic maximum mass Mmax,GRdense∼|λ|MP3/m2. Dense axion stars explode below a Newtonian minimum mass Mmin,Ndense=98.9m/|λ| and form dilute axion stars of large size or disperse away. We determine the phase diagram of self-gravitating axions and show the existence of a triple point (|λ|*,M*/(MP2/m)) separating dilute axion stars, dense axion stars, and black holes. We make numerical applications for QCD axions and ultralight axions. Our approximate analytical results are in good agreement with the exact numerical results of Braaten et al. [Phys. Rev. Lett. 117, 121801 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.121801] for Newtonian dense axion stars. They are also qualitatively similar to those obtained by Helfer et al. [J. Cosmol. Astropart. Phys. 03 (2017) 055JCAPBP1475-751610.1088/1475-7516/2017/03/055] for general relativistic axion stars, but they differ quantitatively for weak self-interactions presumably due to the use of a different self-interaction potential V(|ψ|2). We point out analogies between the evolution of self-gravitating axions (bosons) at zero temperature evolving from dilute axion stars to dense axion stars and black holes and the evolution of compact degenerate (fermion) stars at zero temperature evolving from white dwarfs to neutron stars and black holes. We also discuss some analogies between the phase transitions of Newtonian axion stars at zero temperature and the phase transitions of Newtonian self-gravitating fermions at nonzero temperature. Finally, we suggest that a dense axionic nucleus may form at the center of dark matter halos through the collapse of a dilute axionic core (soliton) passing above the maximum mass Mmax,Ndilute. It would have a mass 1.11×109(f/m)M⊙, a radius 0.949/(mf1/3) pc, a density 2.10×10-8(m2f2) g/m3, a pulsation period 8.24/(mf1/3) yr, and an energy -5.59×1062(f/m) erg, where the axion mass m is measured in units of 10-22 eV/c2 and the axion decay constant f is measured in units of 1015 GeV. This dense axionic nucleus could be the remnant of a bosenova associated with the emission of a characteristic radiation [Phys. Rev. Lett. 118, 011301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.011301].

Using Nottale’s theory of scale relativity, we derive a generalized Schrodinger equation applying to dark matter halos. This equation involves a logarithmic nonlinearity associated with an effective temperature and a source of dissipation. Fundamentally, this wave equation arises from the nondifferentiability of the trajectories of the dark matter particles whose origin may be due to ordinary quantum mechanics, classical ergodic (or almost ergodic) chaos, or to the fractal nature of spacetime at the cosmic scale. The generalized Schrodinger equation involves a coefficient D , possibly different from ħ ∕ 2 m (where ħ is the Planck constant and m the mass of the particles), whose value for dark matter halos is D = 1 . 02 × 1 0 23 m2/s. This model is similar to the Bose–Einstein condensate dark matter model except that it does not require the dark matter particle to be ultralight. It can accommodate any type of particles provided that they have nondifferentiable trajectories. We suggest that the cold dark matter crisis may be solved by the fractal (nondifferentiable) structure of spacetime at the cosmic scale, or by the chaotic motion of the particles on a very long timescale, instead of ordinary quantum mechanics. The equilibrium states of the generalized Schrodinger equation correspond to configurations with a core-halo structure. The quantumlike potential generates a solitonic core that solves the cusp problem of the classical cold dark matter model. The logarithmic nonlinearity accounts for the presence of an isothermal halo that leads to flat rotation curves (it also accounts for the isothermal core of large dark matter halos). The damping term ensures that the system relaxes towards an equilibrium state. This property is guaranteed by an H -theorem satisfied by a Boltzmann-like free energy functional. In our approach, the temperature and the friction arise from a single formalism. They correspond to the real and imaginary parts of the complex friction coefficient present in the scale covariant equation of dynamics that is at the basis of Nottale’s theory of scale relativity. They may be the manifestation of a cosmic aether or the consequence of a process of violent relaxation and gravitational cooling on a coarse-grained scale.

The factorization and resummation approach of Nagar and Shah~[Phys.~Rev.~D~94 (2016), 104017], designed to improve the strong-field behavior of the post-Newtonian (PN) residual waveform amplitudes $f_{\ell m}$'s entering the effective-one-body, circularized, gravitational waveform for spinning coalescing binaries, is here improved and generalized to all multipoles up to $\ell=6$. For a test-particle orbiting a Kerr black hole, each multipolar amplitude is truncated at relative 6~post Newtonian (PN) order, both for the orbital (nonspinning) and spin factors. By taking a certain Pad\'e approximant (typically the $P^4_2$ one) of the orbital factor in conjuction with the inverse Taylor (iResum) representation of the spin factor, it is possible to push the analytical/numerical agreement of the energy fluxe at the level of $5\%$ at the last-stable-orbit for a quasi-maximally spinning black hole with dimensionless spin parameter $+0.99$. When the procedure is generalized to comparable-mass binaries, each orbital factor is kept at relative $3^{+3}$PN order, i.e. the 3PN comparable-mass terms are hybridized with higher PN test-particle terms up to 6PN relative order. The same Pad\'e resummation is used for continuity. By contrast, the spin factor is only kept at the highest comparable-mass PN-order currently available. We illustrate that the consistency between different truncations in the spin content of the waveform amplitudes is stronger in the resummed case than when using the standard Taylor-expanded form of Pan et al.~[Phys.~Rev.~D~83 (2011) 064003]. We finally introduce a method to consistently hybridize comparable-mass and test-particle information {\it also} in the presence of spin (including the spin of the particle), discussing it explicitly for the $\ell=m=2$ spin-orbit and spin-square terms., Comment: 22 pages, 5 figures, submitted to Phys. Rev. D

We present a comprehensive comparison of the spin-aligned effective-one-body (EOB) waveform model of Nagar et al. [Phys. Rev. D93, 044046 (2016)], informed using 40 numerical-relativity (NR) datasets, against a set of 149, $\ell=m=2$, NR waveforms freely available through the Simulation Extreme Spacetime (SXS) catalog. We find that, without further calibration, these EOBNR waveforms have unfaithfulness (at design Advanced-LIGO sensitivity and evaluated with total mass $M$ varying as $10M_\odot\leq M \leq 200M_\odot$) always below $1\%$ against all NR waveforms except for three outliers, that still never exceed the $3\%$ level; with a minimal retuning of the (effective) next-to-next-to-next-to-leading-order spin-orbit coupling parameter for the non-equal-mass and non-equal-spin sector, that only needs three more NR waveforms, one is left with another two (though different) outliers, with maximal unfaithfulness of up to only $2\%$ for a total mass of $200M_\odot$. We show this is the effect of slight inaccuracies in the phenomenological description of the postmerger waveform of Del Pozzo and Nagar [arXiv:1606.03952] that was constructed by interpolating over only 40NR simulations. We argue that this is easily fixed by using either an alternative ringdown description (e.g., the superposition of quasi-normal-modes) or an improved version of the phenomenological representation. By analyzing a NR waveform with mass ratio $8$ and dimensionless spins $+0.85$ obtained with the BAM code, we conclude that the model would benefit from NR simulations specifically targeted at improving the postmerger-ringdown phenomenological fits for mass ratios $\gtrsim 8$ and spins $\gtrsim 0.8$., Comment: 24 pages, 20 figures, submitted to Phys. Rev. D

By post-Newtonian (PN) expanding the well-known, factorized and resummed, effective-one-body energy flux for circularized binaries we show that: (i) because of the presence of the resummed tail factor, the 4.5PN-accurate tails-of-tails-of-tails contribution to the energy flux recently computed by Marchand et al. [Class. Q. Grav. 33 (2016) 244003] is actually contained in the resummed expression; this is also the case of the the next-to-leading-order tail-induced spin-orbit term of Marsat et al. [Class. Q. Grav. 31 (2014) 025023]; (ii) in performing this expansion, we also obtain, for the first time, the explicit 3.5PN leading-order tail-induced spin-spin flux term; (iii) pushing the PN expansion of the (nonspinning) EOB flux up to 5.5PN order, we compute 4PN, 5PN and 5.5PN contributions to the energy flux, though in a form that explicitly depends on, currently unknown, 4PN and 5PN non-test-mass corrections to the factorized waveform amplitudes. Within this (parametrized) 4.5PN accuracy, we calculate the TaylorF2 approximant. Focusing for simplicity on the nonspinning case and using the numerical-relativity calibrated IMRPhenomD waveform model as benchmark, we demonstrate that it is possible to reproduce the derivative of the IMRPhenomD phase (say up to the frequency of the Schwarzschild last-stable-orbit) by flexing only a 4PN "effective" waveform amplitude parameter. A preliminary analysis also illustrates that similar results can be obtained for the spin-aligned case provided only the leading-order spin-orbit and spin-spin terms are kept. Our findings suggest that this kind of, EOB-derived, (parametrized), higher-order, PN approximants may serve as promising tools to construct Inspiral-Merger-Ringdown phenomenological models or even to replace the standardly used 3.5PN-accurate TaylorF2 approximant in searches of small-mass binaries., 11 pages, 3 figures. This version corrects an error in the 4PN term of the TaylorF2 parametrized approximant. The results are however qualitatively unchanged. Incorporates corrections appearing in the various errata published on Phys. Rev. D

Building on the analytical description of the post-merger (ringdown) waveform of coalescing, non-precessing, spinning, (BBHs) introduced in Phys. Rev. D 90, 024054 (2014), we propose an analytic, closed form, time-domain, representation of the $\ell=m=2$ gravitational radiation mode emitted after merger. This expression is given as a function of the component masses and dimensionless spins $(m_{1,2},\chi_{1,2})$ of the two inspiralling objects, as well as of the mass $M_{\rm BH}$ and (complex) frequency $\sigma_{1}$ of the fundamental quasi-normal mode of the remnant black hole. Our proposed template is obtained by fitting the post-merger waveform part of several publicly available numerical relativity simulations from the Simulating eXtreme Spacetimes (SXS) catalog and then suitably interpolating over (symmetric) mass ratio and spins. We show that this analytic expression accurately reproduces ($\sim$~0.01 rad) the phasing of the post-merger data of other datasets not used in its construction. This is notably the case of the spin-aligned run SXS:BBH:0305, whose intrinsic parameters are consistent with the 90\% credible intervals reported by the parameter-estimation followup of GW150914 in Phys. Rev. Lett. 116 (2016) no.24, 241102. Using SXS waveforms as "experimental" data, we further show that our template could be used on the actual GW150914 data to perform a new measure the complex frequency of the fundamental quasi-normal mode so to exploit the complete (high signal-to-noise-ratio) post-merger waveform., Comment: 14 pages, 7 figures, submitted to Phys. Rev. D. Revised and more detailed version. Results unchanged