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In any scalar-tensor theory of gravity exhibiting a screening mechanism, the fifth force mediated by the scalar field is dynamically suppressed at sub-Solar system scales, allowing it to pass existing tests of gravity. As a result, a major research effort has been carried out over the past decades to 'outsmart' screened scalars in this game of hide-and-seek. While most of such tests rely on fifth force effects, one should keep in mind that the latter are by no means the only physical feature of scalar-tensor gravity. In particular, this article investigates the possibility of testing screened scalar-tensor models by means of gravitational redshift measurements performed with atomic clocks. Upon deriving the expression for the redshift in this framework, we propose a thought experiment for testing the chameleon model by clock comparisons, which guides us towards more realistic experimental setups, in the laboratory and in space. We find that the current level of precision exhibited by leading-edge technology is still too low to yield competitive constraints on the chameleon model., Comment: 22 pages, 8 figures

Fundamental constants are a cornerstone of the physical laws. Any constant varying in space and/or time would signal a violation of local position invariance and be associated with a violation of the universality of free fall, and hence of the weak equivalence principle. It will reflect the existence of new degrees of freedom that couple to standard matter. Thus, testing for the stability of fundamental constants is of utmost importance for our understanding of gravity and for characterizing the domain of validity of General Relativity. Besides, it opens an independent window on dark matter and dark energy. As a consequence, thanks to the active development of experiments and of their accuracy, fundamental constants have become a key player in our search for physics beyond the standard model of and beyond General Relativity. This review details the roles of the fundamental constants in the laws of physics and in the construction of the International System of units. Then, the relations between constants, tests of the local position invariance and of the universality of free fall are exposed, as well as the construction of field theories that account for "varying constants". Then, the main experimental and observational constraints are described. It details the basics of each system, its dependence with respect to the primary parameters the variation of which can be constrained from observations, the known systematics effects and the most recent constraints. It also describes how these primary parameters can be related to the fundamental constants and the model-dependencies. Both time and space variation are considered. Given the huge increase of data and constraints, a general scheme to present experimental and observational results and to construct a collaborative data base that will be more efficient for the community and allow for better traceability, is proposed., Comment: Updated and (major) revised version of the review arXiv:1009.5514 initially published as Living Rev. Rel. 14 (2011) 2 under the title "Varying Constants, Gravitation and Cosmology" [collection: Experimental Foundations of Gravitation]. 339 pages, 40 figures

This article demonstrates that additionally to the well-known velocity memory effect, a vacuum gravitational plane wave can also induce a displacement memory on a couple of test particles. A complete classification of the conditions under which a velocity or a displacement memory effect occur is established. These conditions depend both the initial conditions of the relative motion and on the wave profile. The two cases where the wave admits a pulse or a step profile are treated. Our analytical expressions are then compared to numerical integrations to exhibit either a velocity or a displacement memory, in the case of these two families of profiles. Additionally to this classification, the existence of a new symmetry of polarized vacuum gravitational plane wave under M\"{o}bius reparametrization of the null time is demonstrated. Finally, we discuss the resolution of the geodesic deviation equation by means of the underlying symmetries of vacuum gravitational plane wave., Comment: 34+6 pages, 6 figures, references added, typos corrected, accepted version in JCAP

We study lensing of gravitational waves by a black hole in the deep wave optics regime, i.e. when the wavelength is much larger than the black hole Schwarzschild radius. We apply it to triple systems, with a binary of stellar mass objects in the inspiraling phase orbiting around a central massive black hole. We describe the full polarisation structure of the wave and derive predictions for the polarisation modes of the scattered wave measured by the observer. We show that lensing in the wave optics regime is not helicity preserving, as opposed to lensing in the geometric optics regime. The amplitude of the total wave is modulated due to interference between the directly transmitted and lensed components. The relative amplitude of the modulation is fixed by the lensing geometry and can reach unity in the most favourable settings. This indicates that wave optics lensing is potentially detectable by LISA for sufficiently high SNR systems. Our findings show that in the wave optics regime it is necessary to go beyond the usual lensing description where the amplification factor is assumed to be the same for both helicity modes. While motivated by GW190521 and the AGN formation scenario, our results apply more broadly to stellar-mass binaries orbiting a third body described as a Schwarzschild black hole, with a period comparable to the GW observation time., Comment: 26 pages, 8 figures

A family of simple and minimal extensions of the standard cosmological $\Lambda$CDM model in which dark matter experiences an additional long-range scalar interaction is demonstrated to alleviate the long lasting Hubble-tension while letting primordial nucleosynthesis predictions unaffected and passing by construction all current local tests of general relativity. This article describes their theoretical formulation and their implications for dark matter. Then, it investigates their cosmological signatures, both at the background and perturbation levels. A detailed comparison to astrophysical data is performed to discuss their ability to fit existing data. A thorough discussion of the complementarity of the low- and high-redshift data and on their constraining power highlights how these models improve the predictions of the $\Lambda$CDM model whatever the combination of datasets used and why they can potentially resolve the Hubble tension. Being fully predictive in any environment, they pave the way to a better understanding of gravity in the dark matter sector., Comment: 16 figures, 26 pages

A simple and minimal extension of the standard cosmological $\Lambda$CDM model in which dark matter experiences an additional long-range scalar interaction is demonstrated to alleviate the long lasting Hubble-tension while letting primordial nucleosynthesis predictions unaffected and passing by construction all current local tests of general relativity. The theoretical formulation of this $\Lambda\beta$CDM model and its comparison to astrophysical observations are presented to prove its ability to fit existing data and potentially resolve the tension., Comment: 3 figures, 6 pages. arXiv admin note: text overlap with arXiv:2312.12408

Scalar-tensor theories with screening mechanisms come with non-linearities that make it difficult to study setups of complex geometry without resorting to numerical simulations. In this article, we use the $\textit{femtoscope}$ code that we introduced in a previous work in order to compute the fifth force arising in the chameleon model in the Earth orbit. We go beyond published works by introducing a departure from spherical symmetry $\unicode{x2014}$ embodied by a mountain on an otherwise spherical Earth $\unicode{x2014}$ as well as by implementing several atmospheric models, and quantify their combined effect on the chameleon field. Building on the numerical results thus obtained, we address the question of the detectability of a putative chameleon fifth force by means of space geodesy techniques and, for the first time, quantitatively assess the back-reaction created by the screening of a satellite itself. We find that although the fifth force has a supposedly measurable effect on the dynamics of an orbiting spacecraft, the imprecise knowledge of the mass distribution inside the Earth greatly curtails the constraining power of such space missions. Finally, we show how this degeneracy can be lifted when several measurements are performed at different altitudes., Comment: 36 pages, 20 figures. Accepted for publication in PRD

Quantum Rutherford scattering and scattering of classical waves off Coulomb-like potentials have similar formal structures and can be studied using the same mathematical techniques. In both contexts, the long-range nature of the interaction leads to a divergent total cross-section, which has been interpreted and regularized in various ways in the past literature. We review in detail the origin of this divergence, in both real and multipole spaces, and show that it arises from incorrectly using approximations out of their domain of validity. We also stress that although classical and quantum Rutherford scattering share the same formalism, the natures of the associated physical observables differ. We comment on the role of interference: while interference can be safely neglected in a quantum context (due to the fact that the observable quantity is a flux, and the incoming flux is collimated), in a classical context one expects to see a superposition of transmitted and scattered waves in a broad region downstream of the target, hence a cross-section is not connected to any physically observable quantity., Comment: 15 pages, 6 figures

A large class of scalar-tensor theories of gravity exhibit a screening mechanism that dynamically suppresses fifth forces in the Solar system and local laboratory experiments. Technically, at the scalar field equation level, this usually translates into nonlinearities which strongly limit the scope of analytical approaches. This article presents $femtoscope$ $-$ a Python numerical tool based on the Finite Element Method (FEM) and Newton method for solving Klein-Gordon-like equations that arise in particular in the symmetron or chameleon models. Regarding the latter, the scalar field behavior is generally only known infinitely far away from the its sources. We thus investigate existing and new FEM-based techniques for dealing with asymptotic boundary conditions on finite-memory computers, whose convergence are assessed. Finally, $femtoscope$ is showcased with a study of the chameleon fifth force in Earth orbit., Comment: 35 pages, 20 figures, 2 tables. Accepted for publication in PRD

We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schr\"{o}dinger algebra sh(1) = sl$(2,\mathbb{R}) \ltimes \mathcal{H}$. The central charge is given by the black hole mass, echoing results on black hole entropy from near-horizon diffeomorphism symmetry. The finite symmetry transformations generated by these conserved charges correspond to Galilean and conformal transformations of the static field and of the coordinates. This new structure allows one to discuss the static response of a Schwarzschild black hole in the test field approximation from a symmetry-based approach. First we show that the (horizontal) symmetry protecting the vanishing of the Love numbers recently exhibited by Hui et al, dubbed the HJPSS symmetry, coincides with one of the sl$(2,\mathbb{R})$ generators of the Schr\"{o}dinger group. Then, it is demonstrated that the HJPSS symmetry is selected thanks to the spontaneous breaking of the full Schr\"{o}dinger symmetry at the horizon down to a simple abelian sub-group. The latter can be understood as the symmetry protecting the regularity of the test field at the horizon. In the 4-dimensional case, this provides a symmetry protection for the vanishing of the Schwarzschild Love numbers. Our results trivially extend to the Kerr case., Comment: 22+5 pages, clarifications added on the symmetry criterion, extension to Kerr added in Appendix, version published in JHEP

Nuclear physics experiments give reaction rates that, via modelling and comparison with primordial abundances, constrain cosmological parameters. The error bars of a key reaction, \dpg, were tightened in 2020, bringing to light discrepancies between different analyses and calling for more accurate measurements of other reactions., Comment: 2 pages

While most strong-gravitational-lensing systems may be roughly modelled by a single massive object between the source and the observer, in the details all the structures near the light path contribute to the observed images. These additional contributions, known as line-of-sight effects, are non-negligible in practice. This article proposes a new theoretical framework to model the line-of-sight effects, together with very promising applications at the interface of weak and strong lensing. Our approach relies on the dominant-lens approximation, where one deflector is treated as the main lens while the others are treated as perturbations. The resulting framework is technically simpler to handle than the multi-plane lensing formalism, while allowing one to consistently model any sub-critical perturbation. In particular, it is not limited to the usual external-convergence and external-shear parameterisation. As a first application, we identify a specific notion of line-of-sight shear that is not degenerate with the ellipticity of the main lens, and which could thus be extracted from strong-lensing images. This result supports and improves the recent proposal that Einstein rings might be powerful probes of cosmic shear. As a second application, we investigate the distortions of strong-lensing critical curves under line-of-sight effects, and more particularly their correlations across the sky. We find that such correlations may be used to probe, not only the large-scale structure of the Universe, but also the dark-matter halo profiles of strong lenses. This last possibility would be a key asset to improve the accuracy of the measurement of the Hubble-Lema\^itre constant via time-delay cosmography., Comment: 39+14 pages, 15 figures. v2: discussion improved in sec. 3.2; figs. 4 and 15 updated. v3: minor typos corrected, matches published version; v4, v5: other typos corrected

The MICROSCOPE experiment was designed to test the weak equivalence principle in space, by comparing the low-frequency dynamics of cylindrical "free-falling" test masses controlled by electrostatic forces. We use data taken during technical sessions aimed at estimating the electrostatic stiffness of MICROSCOPE's sensors to constrain a short-range Yukawa deviation from Newtonian gravity. We take advantage of the fact that in the limit of small displacements, the gravitational interaction (both Newtonian and Yukawa-like) between nested cylinders is linear, and thus simply characterised by a stiffness. By measuring the total stiffness of the forces acting on a test mass as it moves, and comparing it with the theoretical electrostatic stiffness (expected to dominate), it is a priori possible to infer constraints on the Yukawa potential parameters. However, we find that measurement uncertainties are dominated by the gold wires used to control the electric charge of the test masses, though their related stiffness is indeed smaller than the expected electrostatic stiffness. Moreover, we find a non-zero unaccounted for stiffness that depends on the instrument's electric configuration, hinting at the presence of patch-field effects. Added to significant uncertainties on the electrostatic model, they only allow for poor constraints on the Yukawa potential. This is not surprising, as MICROSCOPE was not designed for this measurement, but this analysis is the first step to new experimental searches for non-Newtonian gravity in space., Comment: Accepted for publication in CQG's MICROSCOPE special issue

This article is dedicated to the use the MICROSCOPE mission's data to test chameleon theory of gravity. We take advantage of the technical sessions aimed to characterize the electrostatic stiffness of MICROSCOPE's instrument intrinsic to its capacitive measurement system. Any discrepancy between the expected and measured stiffness may result from unaccounted-for contributors, i.e. extra-forces. This work considers the case of chameleon gravity as a possible contributor. It was previously shown that in situations similar to these measurement sessions, a chameleon fifth force appears and acts as a stiffness for small displacements. The magnitude of this new component of the stiffness is computed over the chameleon's parameter space. It allows us to derive constraints by excluding any force inconsistent with the MICROSCOPE data. As expected --since MICROSCOPE was not designed for the purpose of such an analysis--, these new bounds are not competitive with state-of-the-art constraints, but they could be improved by a better estimation of all effects at play in these sessions. Hence our work illustrates this novel technique as a new way of constraining fifth forces., Comment: Submitted to PRD

Recent measurements of the D(p,$\gamma)^3$He, nuclear reaction cross-section and of the neutron lifetime, along with the reevaluation of the cosmological baryon abundance from cosmic microwave background (CMB) analysis, call for an update of abundance predictions for light elements produced during the big-bang nucleosynthesis (BBN). While considered as a pillar of the hot big-bang model in its early days, BBN constraining power mostly rests on deuterium abundance. We point out a new $\simeq1.8\sigma$-tension on the baryonic density, or equivalently on the D/H abundance, between the value inferred on one hand from the analysis of the primordial abundances of light elements and, on the other hand, from the combination of CMB and baryonic oscillation data. This draws the attention on this sector of the theory and gives us the opportunity to reevaluate the status of BBN in the context of precision cosmology. Finally, this paper presents an upgrade of the BBN code PRIMAT., Comment: 10 pages, 4 figures. Accepted in MNRAS

The precision reached by current and forthcoming strong-lensing observations requires to accurately model various perturbations to the main deflector. Hitherto, theoretical models have been developed to account for either cosmological line-of-sight perturbations, or isolated secondary lenses via the multi-plane lensing framework. This article proposes a general formalism to describe multiple lenses within an arbitrary space-time background. The lens equation, and the expressions of the amplification and time delays, are rigorously derived in that framework. Our results may be applied to a wide range of set-ups, from strong lensing in anisotropic cosmologies, to line-of-sight perturbations beyond the tidal regime., Comment: 23+6 pages, 9 figures; v3: enriched sec. 2, matches the version published in Classical and Quantum Gravity, except the addition of an important reference (Schneider 2019); v4: minor typos corrected

This article describes the dynamics of a charge particle in a electromagnetic field in presence of a scalar fifth force. Focusing to the fifth force that would be induced by a chameleon field, the profile of which can be designed properly in the laboratory, it draws its physical effects on the cyclotron motion of a particle in a static and uniform magnetic field. The fifth force induces a drift of the trajectory that is estimated analytically and compared to numerical computations for profiles motivated by the ones of a chameleon field within two nested cylinders. The magnitude of the effect and the detectability of this drift are discussed to argue that this may offer a new experimental design to test small fifth force in the laboratory. More important, at the macroscopic level it induces a current that can in principle also be measured, and would even allow one to access the transverse profile of the scalar field within the cavity. In both cases, aligning the magnetic field with the local gravity field suppresses the effects of Newtonian gravity that would be several order larger than the ones of the fifth force otherwise and the Newtonian gravity of the cavity on the particle is also argued to be negligible. Given this insight, this experimental set-up, with its two effects -- on a single particle and at the macroscopic level -- may require attention to demonstrate its actual feasability in the laboratory., Comment: 16 pages, 21 figures

This article presents a new model-independent constraint for bouncing black hole geometries. Using the thin shell formalism, this constraint sets a bound on the minimal allowed radius of the time-like surface of the collapsing star at the bounce. It follows from this bound that the shell always bounces in an untrapped region or precisely on a trapping horizon. This constraint is of purely kinematical origin as it descends from the continuity of the metric between the geometries describing the interior and exterior of the collapsing object so that it is completely model-independent. The second part of this work investigates the conditions under which an effective extension of the Oppenheimer-Snyder collapse can describe consistent bouncing black hole solutions. We show that on top of the previous kinematical constraint, an additional dynamical condition has to be satisfied in order for the model to admit well-defined black-to-white hole solutions. As expected, this second condition turns out to be model-dependent. The resulting class of models describing bouncing compact objects are characterized by three parameters for the star (mass, initial radius and density) and two quantum parameters descending from the UV-completion of the exterior and interior geometries. The solution space contains (1) bouncing stars and (2) bouncing black holes and (3) a new class of astrophysical objects which alternate between a bouncing star and a bouncing black hole. Finally, we provide an explicit construction of a black-to-white hole bounce using the techniques of spatially closed LQC and discuss the novel properties induced by the presence of the inner horizon in this new framework. This generic framework lays down the foundation for interesting phenomenological investigations concerning the astrophysical properties of these objects, as well as a novel platform for further developments., Comment: V2 - 29 pages, 4 figures, Clarifications on the construction of the model added, typos corrected, matched the version accepted in JCAP

This article investigates the properties of a scalar fifth force that arises in a scalar tensor-theory with a chameleon screening mechanism in the context of gravity space missions like the MICROSCOPE experiment. In such an experiment, the propagation of the chameleon field inside the nested cylinders of the experiment causes a fifth force when the cylinders are not perfectly co-axial. We propose a semi-analytic method to compute the field distribution and the induced fifth force and compare it to a full numerical simulation, in settings where the cylindrical symmetry is broken. The scaling of the fifth force with both the parameters of the model and the geometry of the experiment is discussed. We show that the fifth force is repulsive, hence adds a destabilizing stiffness that should be included in the force budget acting on the detector. This opens the way to a new method to constrain a scalar fifth force in screened models., Comment: Submitted to Phys. Rev. D

This article proposes a generalization of the Oppenheimer-Snyder model which describes a bouncing compact object. The corrections responsible for the bounce are parameterized in a general way so as to remain agnostic about the specific mechanism of singularity resolution at play. It thus develops an effective theory based on a thin shell approach, inferring generic properties of such a UV complete gravitational collapse. The main result comes in the form of a strong constraint applicable to general UV models : if the dynamics of the collapsing star exhibits a bounce, it always occurs below, or at most at the energy threshold of horizon formation, so that only an instantaneous trapping horizon may be formed while a trapped region never forms. This conclusion relies solely on i) the assumption of continuity of the induced metric across the time-like surface of the star and ii) the assumption of a classical Schwarzschild geometry describing the (vacuum) exterior of the star. In particular, it is completely independent of the choice of corrections inside the star which leads to singularity-resolution. The present model provides thus a general framework to discuss bouncing compact objects, for which the interior geometry is modeled either by a classical or a quantum bounce. In the later case, our no-go result regarding the formation of trapped region suggests that additional structure, such as the formation of an inner horizon, is needed to build consistent models of matter collapse describing black-to-white hole bounces. Indeed, such additional structure is needed to keep quantum gravity effects confined to the high curvature regime, in the deep interior region, providing thus a new challenge for current constructions of quantum black-to-white hole bounce models., Comment: 20 pages, Published in JCAP

This article presents an effective quantum extension of the seminal Oppenheimer-Snyder (OS) collapse in which the singularity resolution is modeled using the effective dynamics of the spatially closed loop quantum cosmology. Imposing the minimal junction conditions, namely the Israel-Darmois conditions, we glue this bouncing LQC geometry to the classical vacuum exterior Schwarzschild geometry across a time-like thin-shell. Consistency of the construction leads to several major deviations from the classical OS collapse model. Firstly, no trapped region can form and the bounce occurs always above, or at most at the Schwarzschild radius. Secondly, the bouncing star discussed here admits an IR cut-off, additionally to the UV cut-off and corresponds therefore to a pulsating compact object. Thirdly, the scale at which quantum gravity effects become non-negligible is encoded in the ratio between the UV cut-off of the quantum theory and the IR cut-off, which in turn, encodes the minimal energy density $\rho_{\text{min}}$ of the star prior to collapse. This energy density is no more fixed by the mass and maximal radius as in the classical OS model, but is now a free parameter of the model. In the end, while the present model cannot describe a black-to-white hole bounce as initially suggested by the Planck star model, it provides a concrete realization of a pulsating compact object based on LQC techniques. Consistency of the model shows that its regime of applicability is restricted to Planckian relics while macroscopic stellar objects are excluded. This first minimal construction should serve as a platform for further investigations in order to explore the physics of bouncing compact objects within the framework of loop quantum cosmology., Comment: 30 pages, 7 figures, notation changed, clarifications added in Appendix, published version in PRD

In the literature different approaches have been proposed to compute the anisotropies of the astrophysical gravitational wave background. The different expressions derived, although starting from our work Cusin, Pitrou, Uzan, Phys.Rev.D96, 103019 (2017) [1], seem to differ. This article compares the various theoretical expressions proposed so far and provides a separate derivation based on a Boltzmann approach. We show that all the theoretical formula in the literature are equivalent and boil down to the one of Ref. [1] when a proper matching of terms and integration by parts are performed. The difference between the various predictions presented for anisotropies in a cosmological context can only lie in the astrophysical modeling of sources, and neither in the theory nor in the cosmological description of the large scale structures. Finally we comment on the gauge invariance of expressions., Comment: 6 pages

Precision on primordial abundances, deduced from observations, have now reached the percent level for 4He and deuterium. Precision on big bang nucleosynthesis (BBN) predictions should, hence, reach the same level. The uncertainty on the 4He mass fraction is strongly affected by theoretical uncertainties on the weak reaction rates that interconvert neutrons with protons. All these corrections have been calculated in a self-consistent manner and implemented in a new, and public, Mathematica code PRIMAT, together with an extensive data base of reaction rates. Both can be obtained at http://www2.iap.fr/users/pitrou/primat.htm., Comment: To appear in JPS Conference Proceedings (The 15th International Symposium on Origin of Matter and Evolution of Galaxies)

We speculate on the development and availability of new innovative propulsion techniques in the 2040s, that will allow us to fly a spacecraft outside the Solar System (at 150 AU and more) in a reasonable amount of time, in order to directly probe our (gravitational) Solar System neighborhood and answer pressing questions regarding the dark sector (dark energy and dark matter). We identify two closely related main science goals, as well as secondary objectives that could be fulfilled by a mission dedicated to probing the local dark sector: (i) begin the exploration of gravitation's low-acceleration regime with a man-made spacecraft and (ii) improve our knowledge of the local dark matter and baryon densities. Those questions can be answered by directly measuring the gravitational potential with an atomic clock on-board a spacecraft on an outbound Solar System orbit, and by comparing the spacecraft's trajectory with that predicted by General Relativity through the combination of ranging data and the in-situ measurement (and correction) of non-gravitational accelerations with an on-board accelerometer. Despite a wealth of new experiments getting online in the near future, that will bring new knowledge about the dark sector, it is very unlikely that those science questions will be closed in the next two decades. More importantly, it is likely that it will be even more urgent than currently to answer them. Tracking a spacecraft carrying a clock and an accelerometer as it leaves the Solar System may well be the easiest and fastest way to directly probe our dark environment., Comment: White Paper submitted to ESA's Voyage 2050 call for papers. Reference updated

This article investigates the profile of the scalar field of a scalar-tensor theory subject to the chameleon mechanism in the context of gravity space missions like the MICROSCOPE experiment. It analyses the experimental situations for models with an inverse power law potential that can in principle induce a fifth force inside the satellite, hence either be detected or constrained. As the mass of the scalar field depends on the local matter density, the screening of the scalar field depends crucially on both the parameters of the theory (potential and non-minimal coupling to matter) and on the geometry of the satellite. We calculate the profile of the scalar field in 1-, 2- and 3-dimensional satellite configurations without relying on the thick or thin shell approximations for the scalar field. In particular we consider the typical geometry with nested cylinders which is close to the MICROSCOPE design. In this case we evaluate the corresponding fifth force on a test body inside the satellite. This analysis clarifies previous claims on the detectability of the chameleon force by space-borne experiments., Comment: Submitted to Phys. Rev. D

This article explores the properties (amplitude and shape) of the angular power spectrum of the anisotropies of the astrophysical gravitational wave background (AGWB) focusing on the signatures of the astrophysical models describing sub-galactic physics. It demonstrates that while some parameters have negligible impact others, and in particular the stellar evolution models, the metallicity and the merger time delay distribution can result in relative differences of order 40% in the angular power spectrum of anisotropies in both the LIGO/Virgo and LISA frequency bands. It is also shown that the monopole and the anisotropic components of the AGWB are complementary and sensitive to different astrophysical parameters. It follows that AGWB anisotropies are a new observable with the potential to provide new astrophysical information that can not be accessed otherwise., Comment: 24 pages, 19 figures

We show that the anisotropies of the astrophysical stochastic gravitational wave background in the mHz band have a strong dependence on the modelling of galactic and sub-galactic physics. We explore a wide range of self-consistent astrophysical models for stellar evolution and for the distribution of orbital parameters, all calibrated such that they predict the same number of resolved mergers to fit the number of detections during LIGO/Virgo O1+O2 observations runs. We show that different physical choices for the process of black hole collapse and cut-off in the black hole mass distribution give fractional differences in the angular power spectrum of anisotropies up to 50\% on all angular scales. We also point out that the astrophysical information which can be extracted from anisotropies is complementary to the isotropic background and individual mergers. These results underline the interest in the anisotropies of the stochastic gravitational wave background as a new and potentially rich field of research, at the cross-road between astrophysics and cosmology., Comment: 6 pages, 4 figures; accepted in MNRAS

We investigate the discrepancy pointed out by Jenkins et al. in Ref. [1] between the predictions of anisotropies of the astrophysical gravitational wave (GW) background, derived using different methods in Cusin et al. [2] and in Jenkins et al. [3]. We show that this discrepancy is not due to our treatment of galaxy clustering, contrary to the claim made in Ref. [1] and we show that our modeling of clustering gives results in very good agreement with observations. Furthermore we show that the power law spectrum used in Refs. [1] and [3] to describe galaxy clustering is incorrect on large scales and leads to a different scaling of the multipoles $C_\ell$. Moreover, we also explain that the analytic derivation of the gravitational wave background correlation function in Refs. [1] and [3] is mathematically ill-defined and predicts an amplitude of the angular power spectrum which depends on the (arbitrary) choice of a non-physical cut-off., Comment: 6 pages, 3 figures. Comment about [arXiv:1810.13435], discussion about Limber approximation extended

When a luminous source is extended, its distortions by weak gravitational lensing are richer than a mere combination of magnification and shear. In a recent work, we proposed an elegant formalism based on complex analysis to describe and calculate such distortions. The present article further elaborates this finite-beam approach, and applies it to a realistic cosmological model. In particular, the cosmic correlations of image distortions beyond shear are predicted for the first time. These constitute new weak-lensing observables, sensitive to very-small-scale features of the distribution of matter in the Universe. While the major part of the analysis is performed in the approximation of circular sources, a general method for extending it to noncircular sources is presented and applied to the astrophysically relevant case of elliptic sources., Comment: 14+2 pages, 6 figures

The standard theory of weak gravitational lensing relies on the approximation that light beams are infinitesimal. Our recent work showed that the finite size of sources, and the associated light beams, can cause nonperturbative corrections to the weak-lensing convergence and shear. This article thoroughly investigates these corrections in a realistic cosmological model. The continuous transition from infinitesimal to finite beams is understood, and reveals that the previous results overestimated finite-beam effects due to simplistic assumptions on the distribution of matter in the Universe. In a KiloDegree Survey-like setting, finite-beam corrections to the cosmic shear remain subpercent, while percent-level corrections are only reached on subarcmin scales. This article thus demonstrates the validity of the infinitesimal-beam approximation in the interpretation of current weak-lensing data., Comment: 14+2 pages, 10 figures

The tests of the deviations from Newton's or Einstein's gravity in the Earth neighbourhood are tied to our knowledge of the shape and mass distribution of our planet. On the one hand estimators of these "modified" theories of gravity may be explicitly Earth-model-dependent whilst on the other hand the Earth gravitational field would act as a systematic error. We revisit deviations from Newtonian gravity described by a Yukawa interaction that can arise from the existence of a finite range fifth force. We show that the standard multipolar expansion of the Earth gravitational potential can be generalised. In particular, the multipolar coefficients depend on the distance to the centre of the Earth and are therefore not universal to the Earth system anymore. This offers new ways of constraining such Yukawa interactions and demonstrates explicitly the limits of the Newton-based interpretation of geodesy experiments. In turn, limitations from geodesy data restrict the possibility of testing gravity in space. The gravitational acceleration is described in terms of spin-weighted spherical harmonics allowing us to obtain the perturbing force entering the Lagrange-Gauss secular equations. This is then used to discuss the correlation between geodesy and modified gravity experiments and the possibility to break their degeneracy. Finally we show that, given the existing constraints, a Yukawa fifth force is expected to be sub-dominant in satellite dynamics and space geodesy experiments, as long as they are performed at altitudes greater than a few hundred kilometres. Gravity surveys will have to gain at least two orders of magnitude in instrumental precision before satellite geodesy could be used to improve the current constraints on modified gravity., Comment: submitted to CQG

High precision astrometry now enables to measure the time drift of astrophysical observables in real time, hence providing new ways to probe different cosmological models. This article presents a general derivation of the redshift and direction drifts for general observers. It is then applied to the standard cosmological framework of a Friedmann-Lemaitre space- time including all effects at first order in the cosmological perturbations, as well as in the class of spatially anisotropic universe models of the Bianchi I family. It shows that for a general observer, the direction drift splits into a parallax and an aberration drifts and order of magnitude estimates of these two components are provided. The multipolar decomposition of the redshift and aberration drifts is also derived and shows that the observer's peculiar velocity contributes only as a dipole whereas the anisotropic shear contributes as a quadrupole., Comment: 18 pages, 2 figures

We present the first predictions for the angular power spectrum of the astrophysical gravitational wave background constituted of the radiation emitted by all resolved and unresolved astrophysical sources. Its shape and amplitude depend on both the astrophysical properties on galactic scales and on cosmological properties. We show that the angular power spectrum behaves as $C_{\ell}\propto 1/{\ell}$ on large scales and that relative fluctuations of the signal are of order 30% at 100 Hz. We also present the correlations of the astrophysical gravitational wave background with weak-lensing and galaxy distribution. These numerical results pave the way to the study of a new observable at the crossroad between general relativity, astrophysics and cosmology., Comment: 5 pages, 4 figures

Primordial nucleosynthesis is one of the three historical evidences for the big bang model, together with the expansion of the universe and the cosmic microwave background. Now that the number of neutrino families and the baryonic densities have been fixed by laboratory measurements or CMB observations, the model has no free parameter and its predictions are rigid. Departure from its predictions could provide hints or constraints on new physics or astrophysics in the early universe. Precision on primordial abundances deduced from observations have recently been drastically improved and reach the percent level for both deuterium and helium-4. Accordingly, the BBN predictions should reach the same level of precision. For most isotopes, the dominant sources of uncertainty come from those on the laboratory thermonuclear reactions. This article focuses on helium-4 whose predicted primordial abundance depends essentially on weak interactions which control the neutron-proton ratio. The rates of the various weak interaction processes depend on the experimentally measured neutron lifetime, but also includes numerous corrections that we thoroughly investigate here. They are the radiative, zero-temperature, corrections, finite nucleon mass corrections, finite temperature radiative corrections, weak-magnetism, and QED plasma effects, which are for the first time all included and calculated in a self consistent way, allowing to take into account the correlations between them, and verifying that all satisfy detailed balance. The helium-4 predicted mass fraction is $0.24709\pm0.00017$. In addition, we provide a Mathematica code (PRIMAT) that incorporates, not only these corrections but also a full network of reactions, using the best available thermonuclear reaction rates, allowing the predictions of primordial abundances up to the CNO region., Comment: 56 pages, 31 figures

The existence of a light or massive scalar field with a coupling to matter weaker than gravitational strength is a possible source of violation of the weak equivalence principle. We use the first results on the E\"otv\"os parameter by the MICROSCOPE experiment to set new constraints on such scalar fields. For a massive scalar field of mass smaller than $10^{-12}$ eV (i.e. range larger than a few $10^5$ m) we improve existing constraints by one order of magnitude to $|\alpha|<10^{-11}$ if the scalar field couples to the baryon number and to $|\alpha|<10^{-12}$ if the scalar field couples to the difference between the baryon and the lepton numbers. We also consider a model describing the coupling of a generic dilaton to the standard matter fields with five parameters, for a light field: we find that for masses smaller than $10^{-12}$eV, the constraints on the dilaton coupling parameters are improved by one order of magnitude compared to previous equivalence principle tests., Comment: Matches publlished version. Supplemental material added

The gravitational wave radiation emitted by all, resolved and unresolved, astrophysical sources in the observable universe generates a stochastic background. This background has a directional dependence inherited from the inhomogeneities of the matter distribution. This article proposes a new and independent derivation of the angular dependence of its energy density by focusing on the total gravitational wave signal produced by an ensemble of incoherent sources. This approach clarifies the origin of the angular correlation and the relation between the gravitational wave signal that can be measured by interferometers and the energy density of the stochastic background., Comment: 12 pages

Recent detections of gravitational waves from merging binary black holes opened new possibilities to study the evolution of massive stars and black hole formation. In particular, stellar evolution models may be constrained on the basis of the differences in the predicted distribution of black hole masses and redshifts. In this work we propose a framework that combines galaxy and stellar evolution models and use it to predict the detection rates of merging binary black holes for various stellar evolution models. We discuss the prospects of constraining the shape of the time delay distribution of merging binaries using just the observed distribution of chirp masses. Finally, we consider a generic model of primordial black hole formation and discuss the possibility of distinguishing it from stellar-origin black holes., Comment: 10 pages, 6 figures. Modified to match the version accepted by MNRAS

Following the renewed interest for axions as a dark matter component, we revisit the effects of energy loss by axion emission on the evolution of the first generation of stars. These stars with zero metallicity are supposed to be massive, more compact, and hotter than subsequent generations. It is hence important to extend previous studies restricted to solar metallicity stars. Our analysis first compares the evolution of solar metallicity 8, 10 and 12 M$_\odot$ stars to previous work. We then calculate the evolution of 8 zero metallicity stars with and without axion losses and with masses ranging from 20 to 150 M$_\odot$. For the solar metallicity models, we confirm the disappearance of the blue loop phase for a value of the axion-photon coupling, $g_{a\gamma}=10^{-10} {\rm GeV}^{-1}$. Regarding the Pop. III stars, we show that for $g_{a\gamma}=10^{-10} {\rm GeV}^{-1}$, their evolution is not much affected by axion losses except within the range of masses 80$-$130 M$_\odot$. Such stars show significant differences both in their tracks within the $T_c$-$\rho_c$ diagram and in their central composition (in particular $^{20}$Ne and $^{24}$Mg). We discuss the origin of these modifications from the stellar physics point of view, and their potential observational signatures., Comment: 10 pages, 11 figures, accepted for publication in A&A

The standard theory of weak gravitational lensing relies on the infinitesimal light beam approximation. In this context, images are distorted by convergence and shear, the respective sources of which unphysically depend on the resolution of the distribution of matter---the so-called Ricci-Weyl problem. In this letter, we propose a strong-lensing-inspired formalism to describe the lensing of finite beams. We address the Ricci-Weyl problem by showing explicitly that convergence is caused by the matter enclosed by the beam, regardless of its distribution. Furthermore, shear turns out to be systematically enhanced by the finiteness of the beam. This implies, in particular, that the Kaiser-Squires relation between shear and convergence is violated, which could have profound consequences on the interpretation of weak lensing surveys., Comment: 6 pages, 2 figures, v2: matches published version, some typos corrected

Unresolved and resolved sources of gravitational waves are at the origin of a stochastic gravitational wave background. While the computation of its mean density as a function of frequency in a homogeneous and isotropic universe is standard lore, the computation of its anisotropies requires to understand the coarse graining from local systems, to galactic scales and then to cosmology. An expression of the gravitational wave energy density valid in any general spacetime is derived. It is then specialized to a perturbed Friedmann-Lema\^itre spacetime in order to determine the angular power spectrum of this stochastic background as well as its correlation with other cosmological probes, such as the galaxy number counts and weak lensing. Our result for the angular power spectrum also provides an expression for the variance of the gravitational wave background., Comment: 22 pages, 2 figures

This article extends bimetric formulations of massive gravity to make the mass of the graviton to depend on its environment. This minimal extension offers a novel way to reconcile massive gravity with local tests of general relativity without invoking the Vainshtein mechanism. On cosmological scales, it is argued that the model is stable and that it circumvents the Higuchi bound, hence relaxing the constraints on the parameter space. Moreover, with this extension the strong coupling scale is also environmentally dependent in such a way that it is kept sufficiently higher than the expansion rate all the way up to the very early universe, while the present graviton mass is low enough to be phenomenologically interesting. In this sense the extended bigravity theory serves as a partial UV completion of the standard bigravity theory. This extension is very generic and robust and a simple specific example is described., Comment: 6 pages, uses RevTeX4.1

This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from `Hubble horizons'. It explores to what extent one might be able to probe conditions beyond the visual horizon (which is close in size to the present Hubble radius), thereby showing that visual horizons place major limits on what are observationally testable aspects of a multiverse, if such exists. Indeed these limits largely prevent us from observationally proving a multiverse either does or does not exist. We emphasize that event horizons play no role at all in observational cosmology, even in the multiverse context, despite some claims to the contrary in the literature., Comment: 21 pages, overview for the Acad\'emie des Sciences de Paris, published in the special volume of the Comptes Rendus de l'Acad\'emie "Inflation: theoretical and observational status"

The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we compute, together with the standard 2- point angular correlation functions, the off-diagonal correlators, which are no more vanishing by symmetry. While the energy shift induced by the off-centered position of the observer can be suppressed by a proper choice of the observer velocity, a lensing-like effect on the CMB emission point remains. This latter effect is genuinely geometrical (e.g. non-degenerate with a boost) and reflects in the structure of the off-diagonal correlators. At lowest order in this effect, the temperature and polarisation correlation matrices have non-vanishing diagonal elements, as usual, and all the off-diagonal terms are excited. This particular signature of a local void model allows one, in principle, to disentangle geometrical effects from local kinematical ones in CMB observations., Comment: 49 pages, 8 figures

Modeling the stochastic gravitational wave background from various astrophysical sources is a key objective in view of upcoming observations with ground- and space-based gravitational wave observatories such as Advanced LIGO, VIRGO, eLISA and PTA. We develop a synthetic model framework that follows the evolution of single and binary compact objects in an astrophysical context. We describe the formation and merger rates of binaries, the evolution of their orbital parameters with time and the spectrum of emitted gravitational waves at different stages of binary evolution. Our approach is modular and allows us to test and constrain different ingredients of the model, including stellar evolution, black hole formation scenarios and the properties of binary systems. We use this framework in the context of a particularly well-motivated astrophysical setup to calculate the gravitational wave background from several types of sources, including inspiraling stellar-mass binary black holes that have not merged during a Hubble time. We find that this signal, albeit weak, has a characteristic shape that can help constrain the properties of binary black holes in a way complementary to observations of the background from merger events. We discuss possible applications of our framework in the context of other gravitational wave sources, such as supermassive black holes., Comment: 13 pages, 6 figures. Accepted for publication in Phys. Rev. D. Revised to reflect final version

Over the past century, rooted in the theory of general relativity, cosmology has developed a very successful physical model of the universe: the {\em big-bang model}. Its construction followed different stages to incorporate nuclear processes, the understanding of the matter present in the universe, a description of the early universe and of the large scale structure. This model has been confronted to a variety of observations that allow one to reconstruct its expansion history, its thermal history and the structuration of matter. Hence, what we refer to as the big-bang model today is radically different from what one may have had in mind a century ago. This construction changed our vision of the universe, both on observable scales and for the universe as a whole. It offers in particular physical models for the origins of the atomic nuclei, of matter and of the large scale structure. This text summarizes the main steps of the construction of the model, linking its main predictions to the observations that back them up. It also discusses its weaknesses, the open questions and problems, among which the need for a dark sector including dark matter and dark energy., Comment: 69 pages, introductory lecture notes from the Poincar\'e seminar XX (2015) and Les Houches school "Cosmology after Planck: what is next?" (2016)

The recent detection of the binary black hole merger GW150914 demonstrates the existence of black holes more massive than previously observed in X-ray binaries in our Galaxy. This article explores different scenarios of black hole formation in the context of self-consistent cosmic chemical evolution models that simultaneously match observations of the cosmic star formation rate, optical depth to reionization and metallicity of the interstellar medium. This framework is used to calculate the mass distribution of merging black hole binaries and its evolution with redshift. We also study the implications of the black hole mass distribution for the stochastic gravitational wave background from mergers and from core collapse events., Comment: 10 pages, 8 figures. Accepted in MNRAS

Primordial or big bang nucleosynthesis (BBN) is one of the three historical strong evidences for the big bang model. Standard BBN is now a parameter free theory, since the baryonic density of the Universe has been deduced with an unprecedented precision from observations of the anisotropies of the cosmic microwave background (CMB) radiation. There is a good agreement between the primordial abundances of 4He, D, 3He and 7Li deduced from observations and from primordial nucleosynthesis calculations. However, the 7Li calculated abundance is significantly higher than the one deduced from spectroscopic observations and remains an open problem. In addition, recent deuterium observations have drastically reduced the uncertainty on D/H, to reach a value of 1.6%. It needs to be matched by BBN predictions whose precision is now limited by thermonuclear reaction rate uncertainties. This is especially important as many attempts to reconcile Li observations with models lead to an increased D prediction. Here, we re-evaluates the D(p,g)3He, D(d,n)3He and D(d,p)3H reaction rates that govern deuterium destruction, incorporating new experimental data and carefully accounting for systematic uncertainties. Contrary to previous evaluations, we use theoretical ab initio models for the energy dependence of the S-factors. As a result, these rates increase at BBN temperatures, leading to a reduced value of D/H = (2.45$\pm0.10)\times10^{-5}$ (2$\sigma$), in agreement with observations., Comment: Submitted to Phys. Rev. D. (without the non-essential Tables IV, IX, X and XI provided here)

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integrations of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes., Comment: 37+13 pages, 8 figures. A few typos corrected. Matches published version