arXiv subjects

Francis Bernardeau

Publications and source records attributed to Francis Bernardeau.

At least 55 records · Page 3Linked to original sources

arXiv2015

The joint statistics of mildly non-linear cosmological densities and slopes in count-in-cells

In the context of count-in-cells statistics, the joint probability distribution of the density in two concentric spherical shells is predicted from first first principle for sigmas of the order of one. The agreement with simulation is found to be excellent. This statistics allows us to deduce the conditional one dimensional probability distribution function of the slope within under dense (resp. overdense) regions, or of the density for positive or negative slopes. The former conditional distribution is likely to be more robust in constraining the cosmological parameters as the underlying dynamics is less evolved in such regions. A fiducial dark energy experiment is implemented on such counts derived from Lambda-CDM simulations.

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arXiv2014

Cosmological Perturbation Theory for streams of relativistic particles

Motion equations describing streams of relativistic particles and their properties are explored in detail in the framework of Cosmological Perturbation Theory. Those equations, derived in any metric both in the linear and nonlinear regimes, express the matter and momentum conservation. In this context we extend the setup of adiabatic initial conditions - that was initially performed in the Conformal Newtonian gauge - to the Synchronous gauge. The subhorizon limit of the nonlinear motion equations written in a generic perturbed Friedmann-Lemaître metric is then derived and analyzed. We show in particular that the momentum field $P_{i}(x)$ is always potential in the linear regime and remains so at subhorizon scales in the nonlinear regime. Finally the equivalence principle is exploited to highlight invariance properties satisfied by such a system of equations, extending that known for streams of non-relativistic particles, namely the extended Galilean invariance.

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arXiv2014

Cosmic shear full nulling: sorting out dynamics, geometry and systematics

An explicit full nulling scheme for cosmic shear observations is presented. It makes possible the construction of shear maps from extended source distributions for which the lens distance distribution is restricted to a definite interval. Such a construction allows to build totally independent shear maps, at all scales, that can be taken advantage of to constrain background cosmological parameters and systematics using the full statistical power of cosmic shear observations. Another advantage of such construction is that, as the lens redshift distribution can be made arbitrarily narrow, scale mixing due to projection effects can be limited allowing controlled predictions on the large scale shear power spectrum from perturbation theory calculations.

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arXiv2014

Regularized cosmological power spectrum and correlation function in modified gravity models

Based on the multi-point propagator expansion, we present resummed perturbative calculations for cosmological power spectra and correlation functions in the context of modified gravity. In a wide class of modified gravity models that have a screening mechanism to recover general relativity (GR) on small scales, we apply the eikonal approximation to derive the governing equation for resummed propagator that partly includes the non-perturbative effect in the high-k limit. The resultant propagator in the high-k limit contains the new corrections arising from the screening mechanism as well as the standard exponential damping. We explicitly derive the expression for new high-k contributions in specific modified gravity models, and find that in the case of f(R) gravity for a currently constrained model parameter, the corrections are basically of the sub-leading order and can be neglected. Thus, in f(R) gravity, similarly to the GR case, we can analytically construct the regularized propagator that reproduces both the resummed high-k behavior and the low-k results computed with standard perturbation theory, consistently taking account of the nonlinear modification of gravity valid at large scales. With the regularized multi-point propagators, we give predictions for power spectrum and correlation function at one-loop order, and compare those with N-body simulations in f(R) gravity model. As an important application, we also discuss the redshift-space distortions and compute the anisotropic power spectra and correlation functions.

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arXiv2014

Non-Gaussian Minkowski functionals & extrema counts in redshift space

In the context of upcoming large-scale structure surveys such as Euclid, it is of prime importance to quantify the effect of peculiar velocities on geometric probes. Hence the formalism to compute in redshift space the geometrical and topological one-point statistics of mildly non-Gaussian 2D and 3D cosmic fields is developed. Leveraging the partial isotropy of the target statistics, the Gram-Charlier expansion of the joint probability distribution of the field and its derivatives is reformulated in terms of the corresponding anisotropic variables. In particular, the cosmic non-linear evolution of the Minkowski functionals, together with the statistics of extrema are investigated in turn for 3D catalogues and 2D slabs. The amplitude of the non-Gaussian redshift distortion correction is estimated for these geometric probes. In 3D, gravitational perturbation theory is implemented in redshift space to predict the cosmic evolution of all relevant Gram-Charlier coefficients. Applications to the estimation of the cosmic parameters sigma(z) and beta=f/b1 from upcoming surveys is discussed. Such statistics are of interest for anisotropic fields beyond cosmology.

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arXiv2014

Density fields and halo mass functions in the Geometrical Adhesion toy Model

In dimension 2 and above, the Burgers dynamics, the so-called "adhesion model" in cosmology, can actually give rise to several dynamics in the inviscid limit. We investigate here the statistical properties of the density field when it is defined by a "geometrical model" associated with this Burgers velocity field and where the matter distribution is fully determined, at each time step, by geometrical constructions. Our investigations are based on a set of numerical experiments that make use of an improved algorithm, for which the geometrical constructions are efficient and robust. In this work we focus on Gaussian initial conditions with power-law power spectra of slope $n$ in the range $-3<n<1$, where a self-similar evolution develops, and we compute the behavior of power spectra, density probability distributions and mass functions. As expected for such dynamics, the density power spectra show universal high-$k$ tails that are governed by the formation of pointlike masses. The two other statistical indicators however show the same qualitative properties as those observed for 3D gravitational clustering. In particular, the mass functions obey a Press-Schechter like scaling up to a very good accuracy in 1D, and to a lesser extent in 2D. Our results suggest that the "geometrical adhesion model", whose solution is fully known at all times, provides a precious tool to understand some of the statistical constructions frequently used to study the development of mass halos in gravitational clustering.

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arXiv2013

The evolution of the large-scale structure of the universe: beyond the linear regime

These lecture notes introduce analytical tools, methods and results describing the growth of cosmological structure beyond the linear regime. The presentation is focused on the single flow regime of the Vlasov-Poisson equation describing the development of gravitational instabilities in a pressureless fluid. These notes include the introduction of diagrammatic representations of the standard perturbation theory with applications to the calculation of the so-called loop contributions to the power spectra. A large part of these notes is devoted to the exploration of the convergence properties of these terms from the contribution of both the long-wave modes and the short-wave modes. The resulting performances of the two-loop corrections of the power spectra are then presented. Finally other avenues that use different methods are explored. In particular it is shown how joint density and profile probability distribution functions can be constructed out of the multiple-variable cumulant generating functions computed at tree order.

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arXiv2013

Describing massive neutrinos in cosmology as a collection of independent flows

A new analytical approach allowing to account for massive neutrinos in the non-linear description of the growth of the large-scale structure of the universe is proposed. Unlike the standard approach in which neutrinos are described as a unique hot fluid, it is shown that the overall neutrino fluid can be equivalently decomposed into a collection of independent flows. Starting either from elementary conservation equations or from the evolution equation of the phase-space distribution function, we derive the two non-linear motion equations that each of these flows satisfies. Those fluid equations describe the evolution of macroscopic fields. We explain in detail the connection between the collection of flows we defined and the standard massive neutrino fluid. Then, in the particular case of adiabatic initial conditions, we explicitly check that, at linear order, the resolution of this new system of equations reproduces the results obtained in the standard approach based on the collisionless Boltzmann hierarchy. Besides, the approach advocated in this paper allows to show how each neutrino flow settles into the cold dark matter flow depending on initial velocities. It opens the way to a fully non-linear treatment of the dynamical evolution of neutrinos in the framework of large-scale structure growth.

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arXiv2013

Statistics of cosmic density profiles from perturbation theory

The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with $Λ$-CDM simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope -- the density difference between adjacent cells -- and its fluctuations is also computed from the two-cells joint PDF; it also compares very well to simulations, in particular in under-dense regions, with a significant reduced cosmic scatter compared to over-dense regions. It is emphasized that this could prove useful when studying the statistical properties of voids as it can serve as a statistical indicator to test gravity models and/or probe key cosmological parameters.

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arXiv2013

Power spectra in the eikonal approximation with adiabatic and non-adiabatic modes

We use the so-called eikonal approximation, recently introduced in the context of cosmological perturbation theory, to compute power spectra for multi-component fluids. We demonstrate that, at any given order in standard perturbation theory, multipoint power spectra do not depend on the large-scale adiabatic modes. Moreover, we employ perturbation theories to decipher how nonadiabatic modes, such as a relative velocity between two different components, damp the small-scale matter power spectrum, a mechanism recently described in the literature. In particular, we do an explicit calculation at 1-loop order of this effect. While the 1-loop result eventually breaks down, we show how the damping effect can be fully captured by the help of the eikonal approximation. A relative velocity not only induces mode damping but also creates large-scale anisotropic modulations of the matter power spectrum amplitude. We illustrate this for the Local Group environment.

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arXiv2013

Resummed propagators in multi-component cosmic fluids with the eikonal approximation

We introduce the eikonal approximation to study the effect of the large-scale motion of cosmic fluids on their small-scale evolution. This approach consists in collecting the impact of the long-wavelength displacement field into a single or finite number of random variables, whose statistical properties can be computed from the initial conditions. For a single dark matter fluid, we show that we can recover the nonlinear propagators of renormalized perturbation theory. These are obtained with no need to assume that the displacement field follows the linear theory. Then we extend the eikonal approximation to many fluids. In particular, we study the case of two non-relativistic components and we derive their resummed propagators in the presence of isodensity modes. Unlike the adiabatic case, where only the phase of small-scale modes is affected by the large-scale advection field, the isodensity modes change also the amplitude on small scales. We explicitly solve the case of cold dark matter-baryon mixing and find that the isodensity modes induce only very small corrections to the resummed propagators.

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arXiv2013

Precision modeling of redshift-space distortions from multi-point propagator expansion

Using a full implementation of resummed perturbation theory (PT) from a multi-point propagator expansion, we put forward new theoretical predictions for the two-point statistics of matter fluctuations in redshift space. The predictions consistently include PT corrections up to the two-loop order and are based on an improved prescription of the redshift-space distortions (RSD) that properly takes into account their non-Gaussian impact from a systematic low-k expansion. In contrast to the previous studies that partly used standard PT calculations, the present treatment is able to provide a consistent prediction for both power spectra and correlation functions. These results are compared with $N$-body simulations with which a very good agreement is found up to the quadrupole moment. The theoretical predictions for the hexadecapole moment of the power spectra are however found to significantly departs from the numerical results at low redshift. We examine this issue and found it to be likely related to an improper modeling of the RSD damping effects on which this moment shows large dependence.

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arXiv2012

Cosmic propagators at two-loop order

We explore the properties of two-point cosmic propagators when Perturbation Theory (PT) loop corrections are consistently taken into account. We show in particular how the interpolation scheme proposed in arXiv:1112.3895 can be explicitly used up to two-loop order introducing the notion of regular parts for the contributing terms. Extending the one-loop results, we then derive and give semi analytical forms of the two-loop contributions for both the cosmic density and velocity propagators. These results are tested against numerical simulations and shown to significantly improve upon one-loop results for redshifts above 0.5. We found however that at lower redshift two-loop order corrections are too large partly due to a strong sensitivity of those terms to the small scale modes. We show that this dependence is expected to be even larger for higher order loop corrections both from theoretical investigations and numerical tests, the latter obtained with Monte Carlo evaluations of the three-loop contributions. This makes small-scale regularization schemes necessary for the use of such higher order corrections.

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arXiv2012

MPTbreeze: A fast renormalized perturbative scheme

We put forward and test a simple description of multi-point propagators (MP), which serve as building-blocks to calculate the nonlinear matter power spectrum. On large scales these propagators reduce to the well-known kernels in standard perturbation theory, while at smaller scales they are suppresed due to nonlinear couplings. Through extensive testing with numerical simulations we find that this decay is characterized by the same damping scale for both two and three-point propagators. In turn this transition can be well modeled with resummation results that exponentiate one-loop computations. For the first time, we measure the four components of the non-linear (two-point) propagator using dedicated simulations started from two independent random Gaussian fields for positions and velocities, verifying in detail the fundamentals of propagator resummation. We use these results to develop an implementation of the MP-expansion for the nonlinear power spectrum that only requires seconds to evaluate at BAO scales. To test it we construct six suites of large numerical simulations with different cosmologies. From these and LasDamas runs we show that the nonlinear power spectrum can be described at the ~ 2% level at BAO scales for redshifts in the range [0-2.5]. We make a public release of the MPTbreeze code with the hope that it can be useful to the community.

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arXiv2012

RegPT: Direct and fast calculation of regularized cosmological power spectrum at two-loop order

We present a specific prescription for the calculation of cosmological power spectra, exploited here at two-loop order in perturbation theory (PT), based on the multi-point propagator expansion. In this approach power spectra are constructed from the regularized expressions of the propagators that reproduce both the resummed behavior in the high-k limit and the standard PT results at low-k. With the help of N-body simulations, we show that such a construction gives robust and accurate predictions for both the density power spectrum and the correlation function at percent-level in the weakly non-linear regime. We then present an algorithm that allows accelerated evaluations of all the required diagrams by reducing the computational tasks to one-dimensional integrals. This is achieved by means of pre-computed kernel sets defined for appropriately chosen fiducial models. The computational time for two-loop results is then reduced from a few minutes, with the direct method, to a few seconds with the fast one. The robustness and applicability of this method are tested against the power spectrum cosmic emulator from which a wide variety of cosmological models can be explored. The fortran program with which direct and fast calculations of power spectra can be done, RegPT, is publicly released as part of this paper.

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arXiv2012

Constructing Regularized Cosmic Propagators

We present a new scheme for the general computation of cosmic propagators that allow to interpolate between standard perturbative results at low-k and their expected large-k resummed behavior. This scheme is applicable to any multi-point propagator and allows the matching of perturbative low-k calculations to any number of loops to their large-k behavior, and can potentially be applied in case of non-standard cosmological scenarios such as those with non-Gaussian initial conditions. The validity of our proposal is checked against previous prescriptions and measurements in numerical simulations showing a remarkably good agreement. Such a generic prescription for multi-point propagators provides the necessary building blocks for the computation of polyspectra in the context of the so-called Gamma-expansion introduced by Bernardeau et al. (2008). As a concrete application we present a consistent calculation of the matter bispectrum at one-loop order.

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arXiv2012

Cosmic shear bispectrum from second-order perturbations in General Relativity

Future lensing surveys will be nearly full-sky and reach an unprecedented depth, probing scales closer and closer to the Hubble radius. This motivates the study of the cosmic shear beyond the small-angle approximation and including general relativistic corrections that are usually suppressed on sub-Hubble scales. The complete expression of the reduced cosmic shear at second order including all relativistic effects was derived in [1]. In the present paper we compute the resulting cosmic shear bispectrum when all these effects are properly taken into account and we compare it to primordial non-Gaussianity of the local type. The new general relativistic effects are generically smaller than the standard non-linear couplings. However, their relative importance increases at small multipoles and for small redshifts of the sources. The dominant effect among these non standard corrections is due to the inhomogeneity of the source redshift. In the squeezed limit, its amplitude can become of the order of the standard couplings when the redshift of the sources is below 0.5. Moreover, while the standard non-linear couplings depend on the angle between the short and long mode, the relativistic corrections do not and overlap almost totally with local type non-Gaussianity. We find that they can contaminate the search for a primordial local signal by f_NL>10.

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arXiv2011

Exact Results for Propagators in the Geometrical Adhesion Model

The Geometrical Adhesion Model (GAM) we described in previous papers provides a fully solved model for the nonlinear evolution of fields that mimic the cosmological evolution of pressureless fluids. In this context we explore the expected late time properties of the cosmic propagators once halos have formed, in a regime beyond the domain of application of perturbation theories. Whereas propagators in Eulerian coordinates are closely related to the velocity field we show here that propagators defined in Lagrangian coordinates are intimately related to the halo mass function. Exact results can be obtained in the 1D case. In higher dimensions, the computations are more intricate because of to the dependence of the propagators on the detailed shape of the underlying Lagrangian-space tessellations, that is, on the geometry of the regions that eventually collapse to form halos. We illustrate these results for both the 1D and the 2D dynamics. In particular we give here the expected asymptotic behaviors obtained for power-law initial power spectra. These analytical results are compared with the results obtained with dedicated numerical simulations.

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