Search

An exciting possibility to constrain dark matter (DM) scenarios is to search for their gravitational imprints on Black Hole (BH) observations. In this paper, we investigate the impact of self-interacting scalar field DM on the shadow radius of a Schwarzschild BH. We implement a self-consistent formulation, paying attention to the enhancement of the DM density due to the BH gravitational influence and the accretion flow onto the BH. First, we calculate the first-order correction to the shadow radius caused by a general DM environment. Then, we apply this perturbative method to the case of self-interacting scalar field DM and derive analytical expressions for the critical impact parameter. We find that self-consistency requirements, involving the lifetime and the mass of the central DM soliton, or the mass and the size of the extended virialized DM halo, ensure that the impact of the DM environment on the shadow radius is below the observational upper bound. This emphasizes the importance of taking into account the self-consistency constraints of the underlying DM scenario, which can strongly limit the range of possible DM density profiles and their impact on the shadow radius., Comment: 12 pages

We consider the phase shift in the gravitational wave signal induced by fast oscillations of scalar dark matter surrounding binary systems, which could be probed by the future experiments LISA and DECIGO. This effect depends on the local matter density and the mass of the dark matter particle. We compare it to the phase shift due to a standard dynamical friction term, which should generically be present. We find that the effect associated with the oscillations only dominates over the dynamical friction for dark matter masses below $10^{-21}$ eV, with masses below $10^{-23}$ eV implying cloud sizes that are too large to be realistic. Moreover, for masses of the order of $10^{-21}$ eV, LISA and DECIGO would only detect this effect for dark matter densities greater than that in the solar system by a factor $10^5$ or $10^4$ respectively. We conclude that this signal can be ignored for most dark matter scenarios unless very dense clouds of very light dark matter are created early in the Universe at a redshift $z\sim 10^4$., Comment: 9 pages

Cosmological studies have now entered Stage IV according to the Dark Energy Task Force prescription, thanks to new missions (Euclid, Rubin Observatory, SRG/eROSITA) that are expected to provide the required ultimate accuracy in the dark energy (DE) equation of state (EoS). However, none of these projects have the power to systematically unveil the galaxy cluster population at $z>1$. There therefore remains the need for an ATHENA-like mission to run independent cosmological investigations and scrutinise the consistency between the results from the $01$. Such samples will allow a detailed modelling of the evolution of cluster physics along with a standalone cosmological analysis. Our results suggest that survey B has the optimal design as it provides greater statistics. Remarkably, high-$z$ clusters, despite representing 15% or less of the full samples, allow a significant reduction of the uncertainty on the cosmological parameters: $\Delta w_a$ is reduced by a factor of 2.3 and $\Delta f_{NL}^{loc}$ by a factor of 3. Inventorying the high-$z$ X-ray cluster population can play a crucial role in ensuring overall cosmological consistency. This will be the major aim of future new-generation ATHENA-like missions., Comment: Accepted for publication in A&A, 17 pages, 18 figures

Black Holes (BH) traversing a dark matter cloud made out of a self-interacting scalar soliton are slowed down by two complementary effects. At low subsonic speeds, the BH accretes dark matter and this is the only source of dragging along its motion, if we neglect the backreaction of the cloud self-gravity. The situation changes at larger supersonic speeds where a shock appears. This leads to the emergence of an additional friction term, associated with the gravitational and scalar pressure interactions and with the wake behind the moving BH. This is a long distance effect that can be captured by the hydrodynamical regime of the scalar flow far away from the BH. This dynamical friction term has the same form as the celebrated Chandrasekhar collisionless result, albeit with a well-defined Coulomb logarithm and a prefactor that is smaller by a factor 2/3. The infra-red cut-off is naturally provided by the size of the scalar cloud, which is set by the scalar mass and coupling, whilst the ultra-violet behaviour corresponds to the distance from the BH where the velocity field is significantly perturbed by the BH, which is determined by pressure effects. As a result, supersonic BH are slowed down by both the accretion drag and the dynamical friction. This effect will be potentially detectable by future gravitational wave experiments as it influences the phase of the gravitational wave signal from inspiralling binaries.

We investigate the imprints of accretion and dynamical friction on the gravitational-wave signals emitted by binary black holes embedded in a scalar dark matter cloud. As a key feature in this work, we focus on scalar fields with a repulsive self-interaction that balances against the self-gravity of the cloud. To a first approximation, the phase of the gravitational-wave signal receives extra correction terms at $-3$PN, $-4$PN and $-5.5$PN orders, relative to the prediction of vacuum general relativity, due to cloud gravity, accretion and dynamical friction. Future observations by LISA and B-DECIGO have the potential to detect these effects for a large range of scalar masses~$m_\mathrm{DM}$ and self-interaction couplings~$\lambda_4$. This would correspond to scenarios with dark matter clouds smaller than $0.1$ pc, which would be difficult to detect by other probes., Comment: 20 pages, 6 figures, 5 tables

We study the formation and evolution of solitons supported by repulsive self-interactions inside extended halos, for scalar-field dark matter scenarios. We focus on the semiclassical regime where the quantum pressure is typically much smaller than the self-interactions. We present numerical simulations, with initial conditions where the halo is described by the WKB approximation for its eigenfunction coefficients. We find that when the size of the system is of the order of the Jeans length associated with the self-interactions, a central soliton quickly forms and makes about 50% of the total mass. However, if the halo is ten times greater than this self-interaction scale, a soliton only quickly forms in cuspy halos where the central density is large enough to trigger the self-interactions. If the halo has a flat core, it takes a longer time for a soliton to appear, after small random fluctuations on the de Broglie wavelength size build up to reach a large enough density. In some cases, we observe the co-existence of several narrow density spikes inside the larger self-interaction-supported soliton. All solitons appear robust and slowly grow, unless they already make up 40% of the total mass. We develop a kinetic theory, valid for an inhomogeneous background, to estimate the soliton growth rate for low masses. It explains the fast falloff of the growth rate as resonances between the ground state and halo excited states disappear. Our results suggest that cosmological halos would show a large scatter for their soliton mass, depending on their assembly history., Comment: 25 pages, 14 figures

We analyse the dynamics of a light scalar field responsible for the $\mu$ term of the Higgs potential and coupled to matter via the Higgs-portal mechanism. We find that this dilaton model is stable under radiative corrections induced by the standard model particle masses. When the background value of the scalar field is stabilised at the minimum of the scalar potential, the scalar field fluctuations only couple quadratically to the massive fields of the standard model preventing the scalar direct decay into standard model particles. Cosmologically and prior to the electroweak symmetry breaking, the scalar field rolls down along its effective potential before eventually oscillating and settling down at the electroweak minimum. These oscillations can be at the origin of dark matter due to the initial misalignment of the scalar field compared to the electroweak minimum, and we find that, when the mass of the scalar field is less than the eV scale and acts as a condensate behaving like dark matter on large scales, the scalar particles cannot thermalise with the standard model thermal bath. As matter couples in a composition-dependent manner to the oscillating scalar, this could lead to a violation of the equivalence principle aboard satellites such as the MICROSCOPE experiment and the next generation of tests of the equivalence principle. Local gravitational tests are evaded thanks to the weakness of the quadratic coupling in the dark matter halo, and we find that, around other sources, these dilaton models could be subject to a screening akin to the symmetron mechanism., Comment: 36 pages, 3 figures

We investigate the flow around a black hole moving through a cloud of self-interacting scalar dark matter. We focus on the large scalar mass limit, with quartic self-interactions, and on the subsonic regime. We show how the scalar field behaves as a perfect gas of adiabatic index $\gamma_{\rm ad}=2$ at large radii while the accretion rate is governed by the relativistic regime close to the Schwarzschild radius. We obtain analytical results thanks to large-radius expansions, which are also related to the small-scale relativistic accretion rate. We find that the accretion rate is greater than for collisionless particles, by a factor $c/c_s \gg 1$, but smaller than for a perfect gas, by a factor $c_s/c \ll 1$, where $c_s$ is the speed of sound. The dynamical friction is smaller than for a perfect gas, by the same factor $c_s/c \ll 1$, and also smaller than Chandrasekhar's result for collisionless particles, by a factor $c_s/(cC)$, where $C$ is the Coulomb logarithm. It is also smaller than for fuzzy dark matter, by a factor $v_0/c \ll 1$.

Fuzzy Dark Matter (FDM) models admit self-similar solutions which are very different from their Cold Dark Matter (CDM) counterparts and do not converge to the latter in the semiclassical limit. In contrast with the familiar CDM hierarchical collapse, they correspond to an inverse-hierarchy blow-up. Constant-mass shells start in the nonlinear regime, at early times, with small radii and high densities, and expand to reach at late times the Hubble flow, up to small linear perturbations. Thus, larger masses become linear first. This blow-up approximately follows the Hubble expansion, so that the central density contrast remains constant with time, although the width of the self-similar profile shrinks in comoving coordinates. As in a gravitational cooling process, matter is ejected from the central peaks through successive clumps. As in wave systems, the velocities of the geometrical structures and of the matter do not coincide, and matter slowly moves from one clump to the next, with intermittent velocity bursts at the transitions. These features are best observed using the density-velocity representation of the nonrelativistic scalar field, or the mass-shell trajectories, than with the Husimi phase-space distribution, where an analogue of the Heisenberg uncertainty principle blurs the resolution in the position or velocity direction. These behaviours are due to the quantum pressure and the wavelike properties of the Schr\"odinger equation. Although the latter has been used as an alternative to N-body simulations for CDM, these self-similar solutions show that the semiclassical limit needs to be handled with care., Comment: 21 pages,10 figures

We present the forward cosmological analysis of an $XMM$ selected sample of galaxy clusters out to a redshift of unity. Following our previous 2018 study based on the dn/dz quantity alone, we perform an upgraded cosmological analysis of the same XXL C1 cluster catalogue (178 objects), with a detailed account of the systematic errors. We follow the ASpiX methodology: the distribution of the observed X-ray properties of the cluster population is analysed in a 3D observable space (count rate, hardness ratio, redshift) and modelled as a function of cosmology. Compared to more traditional methods, ASpiX allows the inclusion of clusters down to a few tens of photons. We obtain an improvement by a factor of 2 compared to the previous analysis by letting the normalisation of the M-T relation and the evolution of the L-T relation free. Adding constraints from the XXL cluster 2-point correlation function and the BAO from various surveys decreases the uncertainties by 23 and 53 % respectively, and 62% when adding both. Switching to the scaling relations from the Subaru analysis, and letting free more parameters, our final constraints are $\sigma_8$ = $0.99^{+0.14}_{-0.23}$, $\Omega_m$ = 0.296 $\pm$ 0.034 ($S_8 = 0.98^{+0.11}_{-0.21}$) for the XXL sample alone. Finally, we combine XXL ASpiX, the XXL cluster 2-point correlation function and the BAO, with 11 free parameters, allowing for the cosmological dependence of the scaling relations in the fit. We find $\sigma_8$ = $0.793^{+0.063}_{-0.12}$, $\Omega_m$ = 0.364 $\pm$ 0.015 ($S_8 = 0.872^{+0.068}_{-0.12}$), but still compatible with Planck CMB at 2.2$\sigma$. The results obtained by the ASpiX method are promising; further improvement is expected from the final XXL cosmological analysis involving a cluster sample twice as large. Such a study paves the way for the analysis of the eROSITA and future Athena surveys., Comment: 20 pages, 10 figures, accepted for publication in A&A, A&A version has the unabridged abstract

We propose a new mechanism for the formation of dark matter clumps in the radiation era. We assume that a light scalar field is decoupled from matter and oscillates harmonically around its vacuum expectation value. We include self-interactions and consider the nonrelativistic regime. The scalar dynamics are described by a fluid approach where the fluid pressure depends on both quantum and self-interaction effects. When the squared speed of sound of the scalar fluid becomes negative, an instability arises and the fluctuations of the scalar energy-density field start growing. They eventually become nonlinear and clumps form. Subsequently, the clumps aggregate and reach a universal regime. Afterwards, they play the role of cold dark matter. We apply this mechanism first to a model with a negative quartic term stabilised by a positive self-interaction of order six, and then to axion monodromy, where a subdominant cosine potential corrects a mass term. In the first case, the squared speed of sound becomes negative when the quartic term dominates, leading to a tachyonic instability. For axion monodromy, the instability starts very slowly after the squared speed of sound first becomes negative and then oscillates around zero. Initially the density perturbations perform acoustic oscillations due to the quantum pressure. Eventually, they start growing exponentially due to a parametric resonance. In both scenarios, the scalar-field clumps span a wide range of scales and masses, running from the size of atoms to that of galactic molecular clouds, and from $10^{-3} \, {\rm gram}$ to thousands of solar masses. Because of finite-size effects, both from the source and the lens, these dark matter clumps are far beyond the reach of microlensing observations., Comment: 40 pages, 19 figures, published version

We study the predictions for the matter redshift-space power spectrum and correlation function of a Lagrangian-space Gaussian ansatz introduced in a previous work. This model is a natural extension of the Zeldovich approximation, where the displacement and velocity power spectra are determined by the equations of motion, instead of being set equal to the linear power spectrum. It does not contain any free parameter. As for the real-space statistics, we find that this Lagrangian-space approach is much more efficient for the correlation functions than for the power spectra. The damping of the BAO oscillations is well recovered but there is a large smooth drift from the simulations in the power spectra. The multipoles of the correlation functions are well recovered on BAO scales, with an accuracy of $2\%$ for $\xi^s_0$ down to $10 h^{-1}$ Mpc, and of $3\%$ for $\xi^s_2$ down to $26 h^{-1}$ Mpc, at $z \geq 0.35$., Comment: 15 pages

We present a new approach to model the gravitational dynamics of large-scale structures. Instead of solving the equations of motion up to a finite perturbative order or building phenomenological models, we follow the evolution of the probability distribution of the displacement and velocity fields within an approximation subspace. Keeping the exact equations of motion with their full nonlinearity, this provides a nonperturbative scheme that goes beyond shell crossing. Focusing on the simplest case of a curl-free Gaussian ansatz for the displacement and velocity fields, we find that truncations of the power spectra on nonlinear scales directly arise from the equations of motion. This leads to a truncated Zeldovich approximation for the density power spectrum, but with a truncation that is not set a priori and with different power spectra for the displacement and velocity fields. The positivity of their auto power spectra also follows from the equations of motion. Although the density power spectrum is only recovered up to a smooth drift on BAO scales, the predicted density correlation function agrees with numerical simulations within $2\%$ from BAO scales down to $7 h^{-1} {\rm Mpc}$ at $z \geq 0.35$, without any free parameter., Comment: 25 pages

We consider scalar dark matter models where the theory has a shift symmetry only broken by the scalar mass term. We restrict ourselves to K-essence kinetic terms where the shift symmetric part of the Lagrangian is a function of the first derivatives of the scalar field only. In the low-amplitude and nonrelativistic regime, which applies on large galactic scales, scalar clouds form solitons with a finite core. Close to the center of galaxies, where a supermassive Black Hole (BH) resides, we analyze the scalar field distribution and the fate of the dark matter soliton when subject to the BH gravitational attraction. We show that the scalar field profile around such a central BH can be described by new oscillatory solutions of a modified Klein-Gordon equation, which generalize the harmonic oscillations of free scalar dark matter in a flat environment and the Jacobi elliptic functions of the $\phi^4$ model. Moreover, we find that, depending on the form of the K-essence kinetic term, regular solutions can be constructed or not, which connect the relativistic ingoing wavelike profile of the scalar field at the BH horizon to the nearly static nonrelativistic soliton at large distance. These profiles have a constant flux and represent the slow infall of scalar matter into the BH. We show that this regular behavior is only possible for K-essence functions that satisfy the usual conditions for the absence of ghosts and gradient instabilities, together with a new restriction on the growth of the kinetic function $K(X)$ for large argument. It turns out that the same conditions of stability guarantee that quantum corrections are tamed, provided that the mass of the scalar field is less than $10^{-3}$ eV and the strong coupling scale of the model $\Lambda$ is much larger than the scalar mass., Comment: 21 pages

In scalar-field dark matter scenarios, a scalar-field soliton could form at the center of galactic halos, around the supermassive black holes that sit at the center of galaxies. Focusing on the large scalar-mass limit, where the soliton is formed by the balance between self-gravity and a repulsive self-interaction, we study the infall of the scalar field onto the central Schwarzschild black hole. We derive the scalar-field profile, from the Schwarzschild radius to the large radii dominated by the scalar cloud. We show that the steady state solution selects the maximum allowed flux, with a critical profile that is similar to the transonic solution obtained for the hydrodynamic case. This finite flux, which scales as the inverse of the self-interaction coupling, is small enough to allow the dark matter soliton to survive for many Hubble times., Comment: 16 pages

Context. Scaling relations between cluster properties embody the formation and evolution of cosmic structure. Intrinsic scatters and correlations between X-ray properties are determined from merger history, baryonic processes, and dynamical state. Aims. We look for an unbiased measurement of the scatter covariance matrix between the three main X-ray observable quantities attainable in large X-ray surveys -- temperature, luminosity, and gas mass. This also gives us the cluster property with the lowest conditional intrinsic scatter at fixed mass. Methods. Intrinsic scatters and correlations can be measured under the assumption that the observable properties of the intra-cluster medium hosted in clusters are log-normally distributed around power-law scaling relations. The proposed method is self-consistent, based on minimal assumptions, and requires neither the external calibration by weak lensing, dynamical, or hydrostatic masses nor the knowledge of the mass completeness. Results. We analyzed the 100 brightest clusters detected in the XXL Survey and their X-ray properties measured within a fixed radius of 300 kpc. The gas mass is the less scattered proxy (~8%). The temperature (~20%) is intrinsically less scattered than the luminosity (~30%) but it is measured with a larger observational uncertainty. We found some evidence that gas mass, temperature and luminosity are positively correlated. Time-evolutions are in agreement with the self-similar scenario, but the luminosity-temperature and the gas mass-temperature relations are steeper. Conclusions. Positive correlations between X-ray properties can be determined by the dynamical state and the merger history of the halos. The slopes of the scaling relations are affected by radiative processes., Comment: 19 pages, in press on Astronomy and Astrophysics; v02: updated XXL series number

We consider models of scalar dark matter with a generic interaction potential and non-canonical kinetic terms of the K-essence type that are subleading with respect to the canonical term. We analyze the low-energy regime and derive, in the nonrelativistic limit, the effective equations of motions. In the fluid approximation they reduce to the conservation of matter and to the Euler equation for the velocity field. We focus on the case where the scalar field mass $10^{-21} \ll m \lesssim 10^{-4} \, {\rm eV}$ is much larger than for fuzzy dark matter, so that the quantum pressure is negligible on cosmological and galactic scales, while the self-interaction potential and non-canonical kinetic terms generate a significant repulsive pressure. At the level of cosmological perturbations, this provides a dark-matter density-dependent speed of sound. At the nonlinear level, the hydrostatic equilibrium obtained by balancing the gravitational and scalar interactions imply that virialized structures have a solitonic core of finite size depending on the speed of sound of the dark matter fluid. For the most relevant potential in $\lambda_4 \phi^4/4$ or K-essence with a $(\partial \phi)^4$ interaction, the size of such stable cores cannot exceed 60 kpc. Structures with a density contrast larger than $10^6$ can be accommodated with a speed of sound $c_s\lesssim 10^{-6}$. We also consider the case of a cosine self-interaction, as an example of bounded nonpolynomial self-interaction. This gives similar results in low-mass and low-density halos whereas solitonic cores are shown to be absent in massive halos., Comment: 25 pages

We propose a simple model that provides a dynamical cancellation mechanism of the vacuum energy density appearing either in the form of a bare cosmological constant, quantum fluctuations of matter fields or the result of phase transitions. This `conformal compensator model' is based on a conformal coupling $A(\varphi)$ between the Einstein and the Jordan frames. This couples a second scalar field $\lambda$ to the trace of the matter energy-momentum tensor, including the bare cosmological constant, and serves as a dynamical Lagrange multiplier. As a result, the scalar $\lambda$ relaxes to a value which cancels the contributions from the vacuum energy density to the Friedmann equation, and adjusts itself to changes of the vacuum energy density after matter phase transitions. This circumvents Weinberg's theorem through the time dependence of the background scalar field $\varphi$. The radiation era, where the vacuum energy is annulled, is recovered in a natural manner. It is also possible to recover the matter era, via a tracking of the matter energy density by the scalar field, as well as the inflationary and dark energy eras, which correspond to regimes where the cancellation mechanism becomes inefficient. This suggests that inflation, dark energy, and the annulation of the vacuum energy density, could be related to the same mechanism. In this setting, the usual fine-tuning of the vacuum energy is avoided, although the onset of the dark energy era at the appropriate time is not explained., Comment: 20 pages

We consider the gravitational Wilsonian effective action at low energy when all the particles of the standard model have decoupled. When the ${\cal R}^2$ terms dominate, the theory is equivalent to a scalar-tensor theory with the universal coupling $\beta=1/\sqrt 6$ to matter for which we present strong lower and upper bounds on the scalaron mass $m$ obtained by using results from the E\"ot-Wash experiment on the modification of the inverse-square law, the observations of the hot gas of galaxy clusters and the Planck satellite data on the neutrino masses. In terms of the range of the scalar interaction mediated over a distance of order $m^{-1}$, this leads to the small interval $4\,\mu m \lesssim m^{-1} \lesssim 68\, \mu m$ within reach of future experimental tests of deviations from Newton's gravitational inverse-square law., Comment: 13 pages. v2: version to appear in PRD. Updated results using Planck 2018 bound on neutrino masses. References added

We investigate the impact of modified-gravity models on the Lyman-$\alpha$ power spectrum. Building a simple analytical modeling, based on a truncated Zeldovich approximation, we estimate the intergalactic medium power spectrum and the Lyman-$\alpha$ flux decrement power spectrum along the line of sight. We recover the results of numerical simulations for $f(R)$-gravity models and present new results for K-mouflage scenarios. We find that the shape of the distortion due to the modified gravity depends on the model, through the scale-dependence or not of their growth rate. This is more clearly seen in the three-dimensional power spectrum than in the one-dimensional power spectrum, where the line-of-sight integration smoothes the deviation. Whilst the Lyman-$\alpha$ power spectrum does not provide competitive bounds for $f(R)$ theories, it could provide useful constraints for the K-mouflage models. Thus, the efficiency of the Lyman-$\alpha$ power spectrum as a probe of modified-gravity scenarios depends on the type of screening mechanism and the related scale dependence it induces. The prospect of a full recovery of the three-dimensional Lyman-$\alpha$ power spectrum from data would also lead to stronger constraints and a better understanding of screening mechanisms., Comment: 25 pages

We investigate cosmological constraints on K-mouflage models of modified gravity. We consider two scenarios: one where the background evolution is free to deviate from $\Lambda$CDM (K-mouflage) and another one which reproduces a $\Lambda$CDM expansion (K-mimic), implementing both of them into the EFTCAMB code. We discuss the main observational signatures of these models and we compare their cosmological predictions to different datasets, including CMB, CMB lensing, SNIa and different galaxy catalogues. We argue about the possibility of relieving the $H_0$ and weak lensing tensions within these models, finding that K-mouflage scenarios effectively ease the tension on the Hubble Constant. Our final 95\% C.L. bounds on the $\epsilon_{2,0}$ parameter that measures the overall departure from $\Lambda$CDM (corresponding to $\epsilon_{2,0}=0$) are $-0.04\leq \epsilon_{2,0} <0$ for K-mouflage and $0< \epsilon_{2,0} <0.002$ for K-mimic. In the former case the main constraining power comes from changes in the background expansion history, while in the latter case the model is strongly constrained by measurements of the amplitude of matter perturbations. The sensitivity of these cosmological constraints closely matches that of solar system probes. We show that these constraints could be significantly tightened with future ideal probes like CORE., Comment: 26 pages, 8 figures

We describe the effects of the cosmological background on the K-mouflage screening properties of an astrophysical structure. We show that the K-mouflage screening of the spatial gradients of the scalar field, i.e. the screening of the fifth force, happens inside a dynamically generated screening radius. This radius is smaller than the location where the quasistatic approximation, i.e. where the spatial gradients exceed the time derivative, holds. Even though this quasistatic radius is much smaller than the size of the matter overdensity, spatial gradients remain well described by the quasistatic approximation up to the horizon. Cosmologically we find that the time derivatives can remain dominant at redshifts $z\gtrsim 2$, when the cosmic web shows a faster growth. Despite the existence of K-mouflage screening, we confirm that the values of the scalar field itself are still dominated by the cosmological background, down to the center of the matter overdensity, and that for instance the time drift of Newton's constant due to the large-scale cosmological evolution highly constrains K-mouflage models., Comment: 14 pages

We describe scalar-bimetric theories where the dynamics of the Universe are governed by two separate metrics, each with an Einstein-Hilbert term. In this setting, the baryonic and dark matter components of the Universe couple to metrics which are constructed as functions of these two gravitational metrics. The scalar field, contrary to dark energy models, does not have a potential whose role is to mimic a late-time cosmological constant. The late-time acceleration of the expansion of the Universe can be easily obtained at the background level in these models by appropriately choosing the coupling functions appearing in the decomposition of the vierbeins for the baryonic and dark matter metrics. We explicitly show how the concordance model can be retrieved with negligible scalar kinetic energy. This requires the scalar coupling functions to show variations of order unity during the accelerated expansion era. This leads in turn to deviations of order unity for the effective Newton constants and a fifth force that is of the same order as Newtonian gravity, with peculiar features. The baryonic and dark matter self-gravities are amplified although the gravitational force between baryons and dark matter is reduced and even becomes repulsive at low redshift. This slows down the growth of baryonic density perturbations on cosmological scales, while dark matter perturbations are enhanced. In our local environment, the upper bound on the time evolution of Newton's constant requires an efficient screening mechanism that both damps the fifth force on small scales and decouples the local value of Newton constant from its cosmological value. This cannot be achieved by a quasi-static chameleon mechanism, and requires going beyond the quasi-static regime and probably using derivative screenings, such as Kmouflage or Vainshtein screening, on small scales., Comment: 35 pages

We analyse the role, on large cosmological scales and laboratory experiments, of the leading curvature squared contributions to the low energy effective action of gravity. We argue for a natural relationship $c_0\lambda^2\simeq 1$ at low-energy between the ${\cal R}^2$ coefficients $c_0$ of the Ricci scalar squared term in this expansion and the dark energy scale $\Lambda=(\lambda M_{\rm Pl})^4$ in four dimensional Planck mass units. We show how the compatibility between the acceleration of the expansion rate of the Universe, local tests of gravity and the quantum stability of the model all converge to select such a relationship up to a coefficient which should be determined experimentally. When embedding this low energy theory of gravity into candidates for its ultraviolet completion, we find that the proposed relationship is guaranteed in string-inspired supergravity models with modulus stabilisation and supersymmetry breaking leading to de Sitter compactifications. In this case, the scalar degree of freedom of ${\cal R}^2$ gravity is associated to a volume modulus. Once written in terms of a scalar-tensor theory, the effective theory corresponds to a massive scalar field coupled with the universal strength $\beta=1/\sqrt{6}$ to the matter stress-energy tensor. When the relationship $c_0\lambda^2\simeq 1$ is realised we find that on astrophysical scales and in cosmology the scalar field is ultralocal and therefore no effect arises on such large scales. On the other hand, the scalar field mass is tightly constrained by the non-observation of fifth forces in torsion pendulum experiments such as E\"ot-Wash. It turns out that the observation of the dark energy scale in cosmology implies that the scalar field could be detectable by fifth force experiments in the near future., Comment: 28 pages. v2: minor changes. version to appear in Phys. Rev. D

Consistency relations of large-scale structures provide exact nonperturbative results for cross-correlations of cosmic fields in the squeezed limit. They only depend on the equivalence principle and the assumption of Gaussian initial conditions, and remain nonzero at equal times for cross-correlations of density fields with velocity or momentum fields, or with the time derivative of density fields. We show how to apply these relations to observational probes that involve the integrated Sachs-Wolfe effect or the kinematic Sunyaev-Zeldovich effect. In the squeezed limit, this allows us to express the three-point cross-correlations, or bispectra, of two galaxy or matter density fields, or weak lensing convergence fields, with the secondary Cosmic Microwave Background (CMB) distortion in terms of products of a linear and a nonlinear power spectrum. In particular, we find that cross-correlations with the integrated Sachs-Wolfe effect show a specific angular dependence. These results could be used to test the equivalence principle and the primordial Gaussianity, or to check the modeling of large-scale structures., Comment: 10 pages

We investigate scalar-tensor theories where matter couples to the scalar field via a kinetically dependent conformal coupling. These models can be seen as the low-energy description of invariant field theories under a global Abelian symmetry. The scalar field is then identified with the Goldstone mode of the broken symmetry. It turns out that the properties of these models are very similar to the ones of ultralocal theories where the scalar-field value is directly determined by the local matter density. This leads to a complete screening of the fifth force in the Solar System and between compact objects, through the ultralocal screening mechanism. On the other hand, the fifth force can have large effects in extended structures with large-scale density gradients, such as galactic halos. Interestingly, it can either amplify or damp Newtonian gravity, depending on the model parameters. We also study the background cosmology and the linear cosmological perturbations. The background cosmology is hardly different from its $\Lambda$-CDM counterpart whilst cosmological perturbations crucially depend on whether the coupling function is convex or concave. For concave functions, growth is hindered by the repulsiveness of the fifth force whilst it is enhanced in the convex case. In both cases, the departures from the $\Lambda$-CDM cosmology increase on smaller scales and peak for galactic structures. For concave functions, the formation of structure is largely altered below some characteristic mass, as smaller structures are delayed and would form later through fragmentation, as in some warm dark matter scenarios. For convex models, small structures form more easily than in the $\Lambda$-CDM scenario., Comment: 38 pages

We investigate how the consistency relations of large-scale structures are modified when the initial density field is not Gaussian. We consider both scenarios where the primordial density field can be written as a nonlinear functional of a Gaussian field and more general scenarios where the probability distribution of the primordial density field can be expanded around the Gaussian distribution, up to all orders over $\delta_{L0}$. Working at linear order over the non-Gaussianity parameters $f_{\rm NL}^{(n)}$ or $S_n$, we find that the consistency relations for the matter density fields are modified as they include additional contributions that involve all-order mixed linear-nonlinear correlations $\langle \prod \delta_L \prod \delta \rangle$. We derive the conditions needed to recover the simple Gaussian form of the consistency relations. This corresponds to scenarios that become Gaussian in the squeezed limit. Our results also apply to biased tracers, and velocity or momentum cross-correlations., Comment: 13 pages

We consider K-mouflage models which are K-essence theories coupled to matter. We analyse their quantum properties and in particular the quantum corrections to the classical Lagrangian. We setup the renormalisation programme for these models and show that K-mouflage theories involve a recursive construction whereby each set of counter-terms introduces new divergent quantum contributions which in turn must be subtracted by new counter-terms. This tower of counter-terms can be constructed by recursion and allows one to calculate the finite renormalised action of the model. In particular, the classical action is not renormalised and the finite corrections to the renormalised action contain only higher derivative operators. We establish an operational criterion for classicality, where the corrections to the classical action are negligible, and show that this is satisfied in cosmological and astrophysical situations for (healthy) K-mouflage models which pass the solar system tests. We also find that these models are quantum stable around astrophysical and cosmological backgrounds. We then consider the possible embedding of the K-mouflage models in an Ultra-Violet completion. We find that the healthy models which pass the solar system tests all violate the positivity constraint which would follow from the unitarity of the putative UV completion, implying that these healthy K-mouflage theories have no UV completion. We then analyse their behaviour at high energy and we find that the classicality criterion is satisfied in the vicinity of a high energy collision implying that the classical K-mouflage theory can be applied in this context. Moreover, the classical description becomes more accurate as the energy increases, in a way compatible with the classicalisation concept., Comment: 39 pages, 6 figures

We present exact kinematic consistency relations for cosmological structures that do not vanish at equal times and can thus be measured in surveys. These rely on cross-correlations between the density and velocity, or momentum, fields. Indeed, the uniform transport of small-scale structures by long wavelength modes, which cannot be detected at equal times by looking at density correlations only, gives rise to a shift in the amplitude of the velocity field that could be measured. These consistency relations only rely on the weak equivalence principle and Gaussian initial conditions. They remain valid in the non-linear regime and for biased galaxy fields. They can be used to constrain non-standard cosmological scenarios or the large-scale galaxy bias., Comment: 5 pages

Super-chameleon models where all types of matter belong to three secluded sectors, i.e. the dark, supersymmetry breaking and matter sectors, are shown to be dynamically equivalent to ultra-local models of modified gravity. In the dark sector, comprising both dark matter and dark energy, the interaction range between the dark energy field and dark matter is constrained to be extremely short, i.e. shorter than the inverse gravitino mass set by supersymmetry breaking. This realises an extreme version of chameleon screening of the dark energy interaction. On the other hand, the baryonic matter sector decouples from the dark energy in a Damour-Polyakov way. These two mechanisms preclude the existence of any modification of gravity locally in the Solar System due to the presence of the super-chameleon field. On larger scales, the super-chameleon can have effects on the growth of structure and the number of dark matter halos. It can also affect the dynamics of galaxies where the fifth force interaction that it induces can have the same order of magnitude as Newton's interaction., Comment: 23 pages, 14 figures. arXiv admin note: text overlap with arXiv:1605.02938

We present a class of modified-gravity theories which we call ultra-local models. We add a scalar field, with negligible kinetic terms, to the Einstein-Hilbert action. We also introduce a conformal coupling to matter. This gives rise to a new screening mechanism which is not entirely due to the non-linearity of the scalar field potential or the coupling function but to the absence of the kinetic term. As a result this removes any fifth force between isolated objects in vacuum. The predictions of these models only depend on a single free function, as the potential and the coupling function are degenerate, with an amplitude given by a parameter $\alpha \lesssim 10^{-6}$, whose magnitude springs from requiring a small modification of Newton's potential astrophysically and cosmologically. This singles out a redshift $z_{\alpha} \sim \alpha^{-1/3} \gtrsim 100$ where the fifth force is the greatest. The cosmological background follows the $\Lambda$-CDM history within a $10^{-6}$ accuracy, while cosmological perturbations are significantly enhanced (or damped) on small scales, $k \gtrsim 2 h {\rm Mpc}^{-1}$ at $z=0$. The spherical collapse and the halo mass function are modified in the same manner. We find that the modifications of gravity are greater for galactic or sub-galactic structures. We also present a thermodynamic analysis of the non-linear and inhomogeneous fifth-force regime where we find that the Universe is not made more inhomogeneous before $z_\alpha$ when the fifth force dominates, and does not lead to the existence of clumped matter on extra small scales inside halos for large masses while this possibility exists for masses $M\lesssim 10^{11} M_\odot$ where the phenomenology of ultra-local models would be most different from $\Lambda$-CDM., Comment: 40 pages, 23 figures, updated references

Weak lensing (WL) promises to be a particularly sensitive probe of both the growth of large scale structure (LSS) as well as the fundamental relation between matter density perturbations and metric perturbations, thus providing a powerful tool with which we may constrain modified theories of gravity (MG) on cosmological scales. Future deep, wide-field WL surveys will provide an unprecedented opportunity to constrain deviations from General Relativity (GR). Employing a three-dimensional (3D) analysis based on the spherical Fourier-Bessel (sFB) expansion, we investigate the extent to which MG theories will be constrained by a typical 3D WL survey configuration including noise from the intrinsic ellipticity distribution $\sigma_{\epsilon}$ of source galaxies. Here we focus on two classes of screened theories of gravity: i) $f(R)$ chameleon models and ii) environmentally dependent dilaton models. We use one-loop perturbation theory combined with halo models in order to accurately model the evolution of matter power-spectrum with redshift in these theories. Using a Fisher information matrix based approach, we show that for an all-sky spectroscopic survey, the parameter $f_{R_0}$ can be constrained in the range $f_{R_0}< 5\times 10^{-6}(9\times 10^{-6})$ for $n=1(2)$ with a 3$\sigma$ confidence level. This can be achieved by using relatively low order angular harmonics $\ell<100$. Including higher order harmonics $\ell>100$ can further tighten the constraints, making them comparable to current solar-system constraints. We also employ a Principal Component Analysis (PCA) in order to study the parameter degeneracies in the MG parameters. Our results can trivially be extended to other MG theories, such as the K-mouflage models. The confusion from intrinsic ellipticity correlation and modification of the matter power-spectrum at small scale due to feedback mechanisms is briefly discussed., Comment: 25 pages. 10 Figures. 4 Tables. Submitted to PRD

We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density $K$ defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator $(\delta g^{00}_{(u)})^n$ at each order $n$. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when $ K'$ is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys., Comment: 36 pages, 8 figures

We study Modified Gravity (MG) theories by modelling the redshifted matter power spectrum in a spherical Fourier-Bessel (sFB) basis. We use a fully non-linear description of the real-space matter power-spectrum and include the lowest-order redshift-space correction (Kaiser effect), taking into account some additional non-linear contributions. Ignoring relativistic corrections, which are not expected to play an important role for a shallow survey, we analyse two different modified gravity scenarios, namely the generalised Dilaton scalar-tensor theories and the $f({R})$ models in the large curvature regime. We compute the 3D power spectrum ${\cal C}^s_{\ell}(k_1,k_2)$ for various such MG theories with and without redshift space distortions, assuming precise knowledge of background cosmological parameters. Using an all-sky spectroscopic survey with Gaussian selection function $\varphi(r)\propto \exp(-{r^2 / r^2_0})$, $r_0 = 150 \, h^{-1} \, {\textrm{Mpc}}$, and number density of galaxies $\bar {\textrm{N}} =10^{-4}\;{\textrm{Mpc}}^{-3}$, we use a $\chi^2$ analysis, and find that the lower-order $(\ell \leq 25)$ multipoles of ${\cal C}^s_\ell(k,k')$ (with radial modes restricted to $k < 0.2 \, h \,{\textrm{Mpc}}^{-1}$) can constraint the parameter $f_{R_0}$ at a level of $2\times 10^{-5} (3\times 10^{-5})$ with $3 \sigma$ confidence for $n=1(2)$. Combining constraints from higher $\ell > 25$ modes can further reduce the error bars and thus in principle make cosmological gravity constraints competitive with solar system tests. However this will require an accurate modelling of non-linear redshift space distortions. Using a tomographic $\beta(a)$-$m(a)$ parameterization we also derive constraints on specific parameters describing the Dilaton models of modified gravity., Comment: 21 pages, 15 Figures, 1 Table, Submitted to MNRAS

We use the cosmic shear data from the Canada-France-Hawaii Telescope Lensing Survey to place constraints on $f(R)$ and {\it Generalized Dilaton} models of modified gravity. This is highly complimentary to other probes since the constraints mainly come from the non-linear scales: maximal deviations with respects to the General-Relativity + $\Lambda$CDM scenario occurs at $k\sim1 h \mbox{Mpc}^{-1}$. At these scales, it becomes necessary to account for known degeneracies with baryon feedback and massive neutrinos, hence we place constraints jointly on these three physical effects. To achieve this, we formulate these modified gravity theories within a common tomographic parameterization, we compute their impact on the clustering properties relative to a GR universe, and propagate the observed modifications into the weak lensing $\xi_{\pm}$ quantity. Confronted against the cosmic shear data, we reject the $f(R)$ $\{ |f_{R_0}|=10^{-4}, n=1\}$ model with more than 99.9% confidence interval (CI) when assuming a $\Lambda$CDM dark matter only model. In the presence of baryonic feedback processes and massive neutrinos with total mass up to 0.2eV, the model is disfavoured with at least 94% CI in all different combinations studied. Constraints on the $\{ |f_{R_0}|=10^{-4}, n=2\}$ model are weaker, but nevertheless disfavoured with at least 89% CI. We identify several specific combinations of neutrino mass, baryon feedback and $f(R)$ or Dilaton gravity models that are excluded by the current cosmic shear data. Notably, universes with three massless neutrinos and no baryon feedback are strongly disfavoured in all modified gravity scenarios studied. These results indicate that competitive constraints may be achieved with future cosmic shear data., Comment: 13 pages, 7 figures, 2 tables

We investigate the effects of a K-mouflage modification of gravity on the dynamics of clusters of galaxies. We extend the description of K-mouflage to situations where the scalar field responsible for the modification of gravity is coupled to a perfect fluid with pressure. We describe the coupled system at both the background cosmology and cosmological perturbations levels, focusing on cases where the pressure emanates from small-scale nonlinear physics. We derive these properties in both the Einstein and Jordan frames, as these two frames already differ by a few percents at the background level for K-mouflage scenarios, and next compute cluster properties in the Jordan frame that is better suited to these observations. Galaxy clusters are not screened by the K-mouflage mechanism and therefore feel the modification of gravity in a maximal way. This implies that the halo mass function deviates from $\Lambda$-CDM by a factor of order one for masses $M\gtrsim 10^{14} \ h^{-1} M_\odot$. We then consider the hydrostatic equilibrium of gases embedded in galaxy clusters and the consequences of K-mouflage on the X-ray cluster luminosity, the gas temperature, and the Sunyaev-Zel'dovich effect. We find that the cluster temperature function, and more generally number counts, are largely affected by K-mouflage, mainly due to the increased cluster abundance in these models. Other scaling relations such as the mass-temperature and the temperature-luminosity relations are only modified at the percent level due to the constraints on K-mouflage from local Solar System tests., Comment: 34 pages

We show that Solar System tests can place very strong constraints on K-mouflage models of gravity, which are coupled scalar field models with nontrivial kinetic terms that screen the fifth force in regions of large gravitational acceleration. In particular, the bounds on the anomalous perihelion of the Moon imposes stringent restrictions on the K-mouflage Lagrangian density, which can be met when the contributions of higher-order operators in the static regime are sufficiently small. The bound on the rate of change of the gravitational strength in the Solar System constrains the coupling strength $\beta$ to be smaller than $0.1$. These two bounds impose tighter constraints than the results from the Cassini satellite and Big Bang Nucleosynthesis. Despite the Solar System restrictions, we show that it is possible to construct viable models with interesting cosmological predictions. In particular, relative to $\Lambda$-CDM, such models predict percent-level deviations for the clustering of matter and the number density of dark matter haloes. This makes these models predictive and testable by forthcoming observational missions., Comment: 15 pages

We present the redshift-space generalization of the equal-time angular-averaged consistency relations between $(\ell+n)$- and $n$-point polyspectra of the cosmological matter density field. Focusing on the case of $\ell=1$ large-scale mode and $n$ small-scale modes, we use an approximate symmetry of the gravitational dynamics to derive explicit expressions that hold beyond the perturbative regime, including both the large-scale Kaiser effect and the small-scale fingers-of-god effects. We explicitly check these relations, both perturbatively, for the lowest-order version that applies to the bispectrum, and nonperturbatively, for all orders but for the one-dimensional dynamics. Using a large ensemble of $N$-body simulations, we find that our squeezed bispectrum relation is valid to better than $20\%$ up to $1h$Mpc$^{-1}$, for both the monopole and quadrupole at $z=0.35$, in a $\Lambda$CDM cosmology. Additional simulations done for the Einstein-de Sitter background suggest that these discrepancies mainly come from the breakdown of the approximate symmetry of the gravitational dynamics. For practical applications, we introduce a simple ansatz to estimate the new derivative terms in the relation using only observables. Although the relation holds worse after using this ansatz, we can still recover it within $20\%$ up to $1h$Mpc$^{-1}$, at $z=0.35$ for the monopole. On larger scales, $k = 0.2 h\mathrm{Mpc}^{-1}$, it still holds within the statistical accuracy of idealized simulations of volume $\sim8h^{-3}\mathrm{Gpc}^3$ without shot-noise error., Comment: 19 pages, 4 figures. arXiv admin note: text overlap with arXiv:1311.4286

We present a comprehensive derivation of linear perturbation equations for different matter species, including photons, baryons, cold dark matter, scalar fields, massless and massive neutrinos, in the presence of a generic conformal coupling. Starting from the Lagrangians, we show how the conformal transformation affects the dynamics. In particular, we discuss how to incorporate consistently the scalar coupling in the equations of the Boltzmann hierarchy for massive neutrinos and the subsequent fluid approximations. We use the recently proposed K-mouflage model as an example to demonstrate the numerical implementation of our linear perturbation equations. K-mouflage is a new mechanism to suppress the fifth force between matter particles induced by the scalar coupling, but in the linear regime the fifth force is unsuppressed and can change the clustering of different matter species in different ways. We show how the CMB, lensing potential and matter power spectra are affected by the fifth force, and find ranges of K-mouflage parameters whose effects could be seen observationally. We also find that the scalar coupling can have the nontrivial effect of shifting the amplitude of the power spectra of the lensing potential and density fluctuations in opposite directions, although both probe the overall clustering of matter. This paper can serve as a reference for those who work on generic coupled scalar field cosmology, or those who are interested in the cosmological behaviour of the K-mouflage model., Comment: 22 pages, 4 figures

We investigate the small-scale static configurations of K-mouflage models defined by a general function $K(\chi)$ of the kinetic terms. The fifth force is screened by the nonlinear K-mouflage mechanism if $K'(\chi)$ grows sufficiently fast for large negative $\chi$. In the general non-spherically symmetric case, the fifth force is not aligned with the Newtonian force. For spherically symmetric static matter density profiles, the results depend on the potential function $W_{-}(y) = y K'(-y^2/2)$, which must be monotonically increasing to $+\infty$ for $y \geq 0$ to guarantee the existence of a single solution throughout space for any matter density profile. Small radial perturbations around these static profiles propagate as traveling waves with a velocity greater than the speed of light. Starting from vanishing initial conditions for the scalar field and for a time-dependent matter density corresponding to the formation of an overdensity, we numerically check that the scalar field converges to the static solution. If $W_{-}$ is bounded, for high-density objects there are no static solutions throughout space, but one can still define a static solution restricted to large radii. Our dynamical study shows that the scalar field relaxes to this static solution at large radii, whereas spatial gradients keep growing with time at smaller radii. If $W_{-}$ is not bounded but non-monotonic, there is an infinite number of discontinuous static solutions but they are not physical and these models are not theoretically sound. Such K-mouflage scenarios provide an example of theories that can appear viable at the cosmological level, for the cosmological background and perturbative analysis, while being meaningless at a nonlinear level for small-scale configurations. This shows the importance of small-scale nonlinear analysis of screening models., Comment: 20 pages

The clustering ratio $\eta$, a large-scale structure observable originally designed to constrain the shape of the power spectrum of matter density fluctuations, is shown to provide a sensitive probe of the nature of gravity in the cosmological regime. We apply this analysis to $F(R)$ theories of gravity using the luminous red galaxy (LRG) sample extracted from the spectroscopic Sloan Digital Sky Survey (SDSS) data release 7 and 10 catalogues. We find that General Relativity (GR), complemented with a Friedmann-Robertson-Walker (FRW) cosmological model with parameters fixed by the Planck satellite, describes extremely well the clustering of galaxies up to $z\sim 0.6$. On large cosmic scales, the absolute amplitude of deviations from GR, $|f_{R_0 }|$, is constrained to be smaller than $4.6 \times 10^{-5}$ at the $95\%$ confidence level. This bound makes cosmological probes of gravity almost competitive with the sensitivity of Solar System tests, although still one order of magnitude less effective than astrophysical tests. We also extrapolate our results to future large surveys like Euclid and show that the astrophysical bound will certainly remain out of reach for such a class of modified-gravity models that only differ from $\Lambda$CDM at low redshifts., Comment: 15 pages, 11 figures, accepted by PRD

We study the cosmology of K-mouflage theories at the background level. We show that the effects of the scalar field are suppressed at high matter density in the early Universe and only play a role in the late time Universe where the deviations of the Hubble rate from its $\Lambda$-CDM counterpart can be of the order five percent for redshifts $1 \lesssim z \lesssim 5$. Similarly, we find that the equation of state can cross the phantom divide in the recent past and even diverge when the effective scalar energy density goes negative and subdominant compared to matter, preserving the positivity of the squared Hubble rate. These features are present in models for which Big Bang Nucleosynthesis is not affected. We analyze the fate of K-mouflage when the nonlinear kinetic terms give rise to ghosts, particle excitations with negative energy. In this case, we find that the K-mouflage theories can only be considered as an effective description of the Universe at low energy below $1$ keV. In the safe ghost-free models, we find that the equation of state always diverges in the past and changes significantly by a few percent since $z\lesssim 1$., Comment: 18 pages

We study structure formation in K-mouflage cosmology whose main feature is the absence of screening effect on quasilinear scales. We show that the growth of structure at the linear level is affected by both a new time dependent Newton constant and a friction term which depend on the background evolution. These combine with the modified background evolution to change the growth rate by up to ten percent since $z\sim 2$. At the one loop level, we find that the nonlinearities of the K-mouflage models are mostly due to the matter dynamics and that the scalar perturbations can be treated at tree level. We also study the spherical collapse in K-mouflage models and show that the critical density contrast deviates from its $\Lambda$-CDM value and that, as a result, the halo mass function is modified for large masses by an order one factor. Finally we consider the deviation of the matter spectrum from $\Lambda$-CDM on nonlinear scales where a halo model is utilized. We find that the discrepancy peaks around $1\ h{\rm Mpc}^{-1}$ with a relative difference which can reach fifty percent. Importantly, these features are still true at larger redshifts, contrary to models of the chameleon-$f(R)$ and Galileon types., Comment: 24 pages

We explicitly test the equal-time consistency relation between the angular-averaged bispectrum and the power spectrum of the matter density field, employing a large suite of cosmological $N$-body simulations. This is the lowest-order version of the relations between $(\ell+n)$-point and $n$-point polyspectra, where one averages over the angles of $\ell$ soft modes. This relation depends on two wave numbers, $k'$ in the soft domain and $k$ in the hard domain. We show that it holds up to a good accuracy, when $k'/k\ll 1$ and $k'$ is in the linear regime, while the hard mode $k$ goes from linear ($0.1\,h\mathrm{Mpc}^{-1}$) to nonlinear ($1.0\,h\mathrm{Mpc}^{-1}$) scales. On scales $k\lesssim 0.4\,h\mathrm{Mpc}^{-1}$, we confirm the relation within the statistical error of the simulations (typically a few percent depending on the wave number), even though the bispectrum can already deviate from leading-order perturbation theory by more than $30\%$. We further examine the relation on smaller scales with higher resolution simulations. We find that the relation holds within the statistical error of the simulations at $z=1$, whereas we find deviations as large as $\sim 7\%$ at $k \sim 1.0\,h\mathrm{Mpc}^{-1}$ at $z=0.35$. We show that this can be explained partly by the breakdown of the approximation $\Omega_\mathrm{m}/f^2\simeq1$ with supplemental simulations done in the Einstein-de Sitter background cosmology. We also estimate the impact of this approximation on the power spectrum and bispectrum., Comment: 14 pages, 15 figures, added Sec. III E and Appendixes, matched to PRD published version

The cosmological dynamics of gravitational clustering satisfies an approximate invariance with respect to the cosmological parameters that is often used to simplify analytical computations. We describe how this approximate symmetry gives rise to angular averaged consistency relations for the matter density correlations. This allows one to write the $(\ell+n)$ density correlation, with $\ell$ large-scale linear wave numbers that are integrated over angles, and $n$ fixed small-scale nonlinear wave numbers, in terms of the small-scale $n$-point density correlation and $\ell$ prefactors that involve the linear power spectra at the large-scale wave numbers. These relations, which do not vanish for equal-time statistics, go beyond the already known kinematic consistency relations. They could be used to detect primordial non-Gaussianities, modifications of gravity, limitations of galaxy biasing schemes, or to help designing analytical models of gravitational clustering., Comment: 16 pages, exact nonlinear results in 1D have been added

We describe how the kinematic consistency relations satisfied by density correlations of the large-scale structures of the Universe can be derived within the usual Newtonian framework. These relations express a kinematic effect and show how the $(\ell+n)$-density correlation factors in terms of the $n$-point correlation and $\ell$ linear power spectrum factors, in the limit where the $\ell$ soft wave numbers become linear and much smaller than the $n$ other wave numbers. We describe how these relations extend to multifluid cases. In the standard cosmology, these consistency relations derive from the equivalence principle. A detection of their violation would indicate non-Gaussian initial conditions, non-negligible decaying modes, or a modification of gravity that does not converge to General Relativity on large scales., Comment: 14 pages

We investigate the possible accuracy that can be reached by analytical models for the matter density power spectrum and correlation function. Using a realistic description of the power spectrum that combines perturbation theory with a halo model, we study the convergence rate of several perturbative expansion schemes and the impact of nonperturbative effects, as well as the sensitivity to phenomenological halo parameters. We check that the simple reorganization of the standard perturbative expansion, with a Gaussian damping prefactor, provides a well-ordered convergence and a finite correlation function that yields a percent accuracy at the baryon acoustic oscillation peak (as soon as one goes to second order). Lagrangian-space expansions are somewhat more efficient, when truncated at low orders, but may diverge at high orders. We find that whereas the uncertainty on the halo-profile mass-concentration relation is not a strong limitation, the uncertainty on the halo mass function can severely limit the accuracy of theoretical predictions for $P(k)$ (this also applies to the power spectra measured in numerical simulations). The real-space correlation function provides a better separation between perturbative and nonperturbative effects, which are restricted to $x \lesssim 10 h^{-1}$Mpc at all redshifts., Comment: 16 pages

We estimate the amplitude of the source-lens clustering bias and of the intrinsic-alignment bias of weak lensing estimators of the two-point and three-point convergence and cosmic-shear correlation functions. We use a linear galaxy bias model for the galaxy-density correlations, as well as a linear intrinsic-alignment model. For the three-point and four-point density correlations, we use analytical or semi-analytical models, based on a hierarchical ansatz or a combination of one-loop perturbation theory with a halo model. For two-point statistics, we find that the source-lens clustering bias is typically several orders of magnitude below the weak lensing signal, except when we correlate a very low-redshift galaxy ($z_2 \la 0.05$) with a higher redshift galaxy ($z_1 \ga 0.5$), where it can reach $10\%$ of the signal for the shear. For three-point statistics, the source-lens clustering bias is typically of order $10\%$ of the signal, as soon as the three galaxy source redshifts are not identical. The intrinsic-alignment bias is typically about $10\%$ of the signal for both two-point and three-point statistics. Thus, both source-lens clustering bias and intrinsic-alignment bias must be taken into account for three-point estimators aiming at a better than $10\%$ accuracy., Comment: 27 pages