arXiv subjects

Francis Bernardeau

Publications and source records attributed to Francis Bernardeau.

At least 37 records · Page 2Linked to original sources

arXiv2020

Tomographic weak lensing bispectrum: a thorough analysis towards the next generation of galaxy surveys

We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum-bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelised prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the 6-point correlation function and super-sample effects. This performance allows us to qualitatively address several interesting scientific questions. We find that the bispectrum provides an improvement in terms of signal-to-noise ratio (S/N) of about 10% on top of the power spectrum, making it a non-negligible source of information for future surveys. Furthermore, we are capable to test the impact of theoretical uncertainties in the halo model used to build our observables; with presently allowed variations we conclude that the impact is negligible on the S/N. Finally, we consider data compression possibilities to optimise future analyses of the weak lensing bispectrum. We find that, ignoring systematics, 5 equipopulated redshift bins are enough to recover the information content of a Euclid-like survey, with negligible improvement when increasing to 10 bins. We also explore principal component analysis and dependence on the triangle shapes as ways to reduce the numerical complexity of the problem.

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arXiv2020

Post-Born corrections to the one-point statistics of (CMB) lensing convergence obtained via large deviation theory

Weak lensing of galaxies and CMB photons through the large-scale structure of the Universe is one of the most promising cosmological probes with upcoming experiments dedicated to its measurements such as Euclid/LSST and CMB Stage 4 experiments. With increasingly precise measurements, there is a dire need for accurate theoretical predictions. In this work, we focus on higher order statistics of the weak lensing convergence field, namely its cumulants such as skewness and kurtosis and its one-point probability distribution (PDF), and we quantify using perturbation theory the corrections coming from post-Born effects, meaning beyond the straight-line and independent lenses approximations. At first order, two such corrections arise: lens-lens couplings and geodesic deviation. Though the corrections are small for low source redshifts (below a few percents) and therefore for galaxy lensing, they become important at higher redshifts, notably in the context of CMB lensing, where the non-gaussianities computed from tree-order perturbation theory are found to be of the same order as the signal itself. We include these post-Born corrections on the skewness into a prediction for the one-point convergence PDF obtained with large deviation theory and successfully test these results against numerical simulations. The modelled PDF is indeed shown to perform better than the percent for apertures above ~ 10 arcminutes and typically in the three sigmas region around the mean.

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arXiv2020

Game of cones: A nulling strategy for modelling lensing convergence in cones with large deviation theory

The distribution of the cosmic convergence field is modeled using a large-deviation principle where all non-Gaussian contributions are computed from first principles. The geometry of the past light cone is accounted for by constructing the total weak-lensing signal from contributions of the matter density in thin disk slices. The prediction of this model is successfully tested against numerical simulation with ray tracing, and found to be accurate within at least 5 per cent in the tails at redshift 1 and opening angle of 10 arcmin and even more so with increasing source redshift and opening angle. An accurate analytical approximation to the theory is also provided for practical implementation. The lensing kernel that mixes physical scales along the line-of-sight tends to reduce the domain of validity of this theoretical approach compared to the three dimensional case of cosmic densities in spherical cells. This effect is shown to be avoidable if a nulling procedure is implemented in order to localise the lensing line-of-sight integrations in a tomographic analysis. Accuracy in the tails is thus achieved within a percent for source redshifts between 0.5 and 1.5 and an opening angle of 10 arcmin. Applications to future weak-lensing surveys like Euclid and the specific issue of shape noise are discussed.

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arXiv2019

Perturbation theory challenge for cosmological parameters estimation: Matter power spectrum in real space

We study the accuracy with which cosmological parameters can be determined from real space power spectrum of matter density contrast at weakly nonlinear scales using analytical approaches. From power spectra measured in $N$-body simulations and using Markov chain Monte-Carlo technique, the best-fitting cosmological input parameters are determined with several analytical methods as a theoretical template, such as the standard perturbation theory, the regularized perturbation theory, and the effective field theory. We show that at redshift 1, all two-loop level calculations can fit the measured power spectrum down to scales $k \sim 0.2 \, h \, \mathrm{Mpc}^{-1}$ and cosmological parameters are successfully estimated in an unbiased way. Introducing the Figure of bias (FoB) and Figure of merit (FoM) parameter, we determine the validity range of those models and then evaluate their relative performances. With one free parameter, namely the damping scale, the regularized perturbation theory is found to be able to provide the largest FoM parameter while keeping the FoB in the acceptance range.

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arXiv2018

k-cut Cosmic Shear: Tunable Power Spectrum Sensitivity to Test Gravity

If left unchecked modeling uncertainties at small scales, due to poorly understood baryonic physics and non-linear structure formation, will significantly bias Stage IV cosmic shear two-point statistic parameter constraints. While it is perhaps possible to run N-body or hydrodynamical simulations to determine the impact of these effects this approach is computationally expensive; especially to test a large number of theories of gravity. Instead we propose directly removing sensitivity to small-scale structure from the lensing spectrum, creating a statistic that is robust to these uncertainties. We do this by taking a redshift-dependent l-cut after applying the Bernardeau-Nishimichi-Taruya (BNT) nulling scheme. This reorganizes the information in the lensing spectrum to make the relationship between the angular scale, l, and the structure scale, k, much clearer compared to standard cosmic shear power spectra -- for which no direct relationship exists. We quantify the effectiveness of this method at removing sensitivity to small scales and compute the predicted Fisher error on the dark energy equation of state, w0, for different k-cuts in the matter power spectrum.

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arXiv2017

Moving around the cosmological parameter space: a nonlinear power spectrum reconstruction based on high-resolution cosmic responses

We present numerical measurements of the power spectrum response function of the gravitational growth of cosmic structures, defined as the functional derivative of the nonlinear spectrum with respect to the linear counterpart, based on $1,400$ cosmological simulations. We develop a simple analytical model based on a regularization of the standard perturbative calculation. Using the model prediction, we show that this function gives a natural way to interpolate the nonlinear power spectrum over cosmological parameter space from single or multi-step interpolations. We demonstrate that once an accurate numerical spectrum template is available for one (or a small number of) cosmological model(s), it doubles the range in $k$ for which percent level accuracy can be obtained even for large change in the cosmological parameters. The python package RESPRESSO we developed to make those predictions is publicly available.

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arXiv2017

Cylinders out of a top hat: counts-in-cells for projected densities

Large deviation statistics is implemented to predict the statistics of cosmic densities in cylinders applicable to photometric surveys. It yields few percent accurate analytical predictions for the one-point probability distribution function (PDF) of densities in concentric or compensated cylinders; and also captures the density-dependence of their angular clustering (cylinder bias). All predictions are found to be in excellent agreement with the cosmological simulation Horizon Run 4 in the quasi-linear regime where standard perturbation theory normally breaks down. These results are combined with a simple local bias model that relates dark matter and tracer densities in cylinders and validated on simulated halo catalogues. This formalism can be used to probe cosmology with existing and upcoming photometric surveys like DES, Euclid or WFIRST containing billions of galaxies.

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arXiv2017

Hunting high and low: Disentangling primordial and late-time non-Gaussianity with cosmic densities in spheres

Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point probability distribution function (PDF) and the two-point clustering of spherically-averaged cosmic densities (sphere bias). Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions. In the presence of primordial non-Gaussianity, sphere bias displays a strong scale dependence relevant for both high and low density regions, which is predicted analytically. The statistics of densities in spheres are built to model primordial non-Gaussianity via an initial skewness with a scale-dependence that depends on the bispectrum of the underlying model. The analytical formulas with the measured nonlinear dark matter variance as input are successfully tested against numerical simulations. For local non-Gaussianity with a range from $f_{\rm NL}=-100$ to $+100$ they are found to agree within 2\% or better for densities $ρ\in[0.5,3]$ in spheres of radius 15 Mpc$/h$ down to $z=0.35$. The validity of the large deviation statistics formalism is thereby established for all observationally relevant local-type departures from perfectly Gaussian initial conditions. The corresponding estimators for the amplitude of the nonlinear variance $σ_8$ and primordial skewness $f_{\rm NL}$ are validated using a fiducial joint maximum likelihood experiment. The influence of observational effects and the prospects for a future detection of primordial non-Gaussianity from joint one- and two-point densities-in-spheres statistics are discussed.

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arXiv2017

Large deviations theory approach to cosmic shear calculations: the one-point aperture mass

This paper presents a general formalism that allows the derivation of the cumulant generating function and one-point Probability Distribution Function (PDF) of the aperture mass ($\hat{M}_{ap}$), a common observable for cosmic shear observations. Our formalism is based on the Large Deviation Principle (LDP) applied, in such cosmological context, to an arbitrary set of densities in concentric cells. We show here that the LDP can indeed be used for a much larger family of observables than previously envisioned, such as those built from continuous and nonlinear functionals of the density profiles. The general expression of the observable aperture mass depends on reduced shear profile making it a rather involved function of the projected density field. Because of this difficulty, an approximation that is commonly employed consists in replacing the reduced shear by the shear in such a construction neglecting therefore non-linear effects. We were precisely able to quantify how this approximation affects the $\hat{M}_{ap}$ statistical properties. In particular we derive the corrective term for the skewness of the $\hat{M}_{ap}$ and reconstruct its one-point PDF.

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arXiv2017

A question of separation: disentangling tracer bias and gravitational nonlinearity with counts-in-cells statistics

Starting from a very accurate model for density-in-cells statistics of dark matter based on large deviation theory, a bias model for the tracer density in spheres is formulated. It adopts a mean bias relation based on a quadratic bias model to relate the log-densities of dark matter to those of mass-weighted dark haloes in real and redshift space. The validity of the parametrised bias model is established using a parametrisation-independent extraction of the bias function. This average bias model is then combined with the dark matter PDF, neglecting any scatter around it: it nevertheless yields an excellent model for densities-in-cells statistics of mass tracers that is parametrised in terms of the underlying dark matter variance and three bias parameters. The procedure is validated on measurements of both the one and two point statistics of subhalo densities in the state-of-the-art Horizon Run 4 simulation showing excellent agreement for measured dark matter variance and bias parameters. Finally, it is demonstrated that this formalism allows for a joint estimation of the nonlinear dark matter variance and the bias parameters using solely the statistics of subhaloes. Having verified that galaxy counts in hydrodynamical simulations sampled on a scale of 10 Mpc/h closely resemble those of subhaloes, this work provides important steps towards making theoretical predictions for density-in-cells statistics applicable to upcoming galaxy surveys like Euclid or WFIRST.

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arXiv2017

Two is better than one: joint statistics of density and velocity in concentric spheres as a cosmological probe

The analytical formalism to obtain the probability distribution functions (PDFs) of spherically-averaged cosmic densities and velocity divergences in the mildly non-linear regime is presented. A large-deviation principle is applied to those cosmic fields assuming their most likely dynamics in spheres is set by the spherical collapse model. We validate our analytical results using state-of-the-art dark matter simulations with a phase-space resolved velocity field finding a 2% percent level agreement for a wide range of velocity divergences and densities in the mildly nonlinear regime (~10Mpc/h at redshift zero), usually inaccessible to perturbation theory. From the joint PDF of densities and velocity divergences measured in two concentric spheres, we extract with the same accuracy velocity profiles and conditional velocity PDF subject to a given over/under-density which are of interest to understand the non-linear evolution of velocity flows. Both PDFs are used to build a simple but accurate maximum likelihood estimators for the redshift evolution of the variance of both the density and velocity divergence fields, which have smaller relative errors than their sample variances when non-linearities appear. Given the dependence of the velocity divergence on the growth rate, there is a significant gain in using the full knowledge of both PDFs to derive constraints on the equation of state of dark energy. Thanks to the insensitivity of the velocity divergence to bias, its PDF can be used to obtain unbiased constraints on the growth of structures ($σ_8$,f) or it can be combined with the galaxy density PDF to extract bias parameters.

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arXiv2016

Response function of the large-scale structure of the universe to the small scale inhomogeneities

In order to infer the impact of the small-scale physics to the large-scale properties of the universe, we use a series of cosmological $N$-body simulations of self-gravitating matter inhomogeneities to measure, for the first time, the response function of such a system defined as a functional derivative of the nonlinear power spectrum with respect to its linear counterpart. Its measured shape and amplitude are found to be in good agreement with perturbation theory predictions except for the coupling from small to large-scale perturbations. The latter is found to be significantly damped, following a Lorentzian form. These results shed light on validity regime of perturbation theory calculations giving a useful guideline for regularization of small scale effects in analytical modeling. Most importantly our result indicates that the statistical properties of the large-scale structure of the universe are remarkably insensitive to the details of the small-scale physics, astrophysical or gravitational, paving the way for the derivation of robust estimates of theoretical uncertainties on the determination of cosmological parameters from large-scale survey observations.

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arXiv2016

Back in the saddle: Large-deviation statistics of the cosmic log-density field

We present a first principle approach to obtain analytical predictions for spherically-averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation principle allows us to compute the leading-order cumulants of average densities in concentric cells. In this symmetry, the spherical collapse model leads to cumulant generating functions that are robust for finite variances and free of critical points when logarithmic density transformations are implemented. They yield in turn accurate density probability distribution functions (PDFs) from a straightforward saddle-point approximation valid for all density values. Based on this easy-to-implement modification, explicit analytic formulas for the evaluation of the one- and two-cell PDF are provided. The theoretical predictions obtained for the PDFs are accurate to a few percent compared to the numerical integration, regardless of the density under consideration and in excellent agreement with N-body simulations for a wide range of densities. This formalism should prove valuable for accurately probing the quasi-linear scales of low redshift surveys for arbitrary primordial power spectra.

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arXiv2016

The large-scale correlations of multi-cell densities and profiles, implications for cosmic variance estimates

In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of their two-point correlation function to the two-point correlation of the underlying dark matter distribution. They describe how cell densities are spatially correlated. They are computed here via the so-called large deviation principle in the quasi-linear regime. Their large-separation limit is presented and successfully compared to simulations for density and density slopes: this regime is shown to be rapidly reached allowing to get sub-percent precision for a wide range of densities and variances. The corresponding asymptotic limit provides an estimate of the cosmic variance of standard concentric cell statistics applied to finite surveys. More generally, no assumption on the separation is required for some specific moments of the two-point statistics, for instance when predicting the generating function of cumulants containing any powers of concentric densities in one location and one power of density at some arbitrary distance from the rest. This exact "one external leg" cumulant generating function is used in particular to probe the rate of convergence of the large-separation approximation.

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arXiv2016

Redshift-space distortions with wide angular separations

Redshift-space distortions are generally considered in the plane parallel limit, where the angular separation between the two sources can be neglected. Given that galaxy catalogues now cover large fractions of the sky, it becomes necessary to consider them in a formalism which takes into account the wide angle separations. In this article we derive an operational formula for the matter correlators in the Newtonian limit to be used in actual data sets, both in configuration and in Fourier spaces without relying on a plane-parallel approximation. We then recover the plane-parallel limit not only in configuration space where the geometry is simpler, but also in Fourier space, and we exhibit the first corrections that should be included in large surveys as a perturbative expansion over the plane-parallel results. We finally compare our results to existing literature, and show explicitly how they are related.

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arXiv2015

A Large Deviation Principle at play in Large-Scale Structure cosmology

We present an application of Large Deviation Theory to the problem of structure growth on large-scale structure cosmology. Starting from gaussian distributed overdensities on concentric spherical shells, we show that a Large Deviation Principle holds for the densities on the corresponding shells after gravitational evolution if no shell-crossing happens. As consequences of the Large Deviation Principle we obtain the cumulant generating function for the non-linear densities, and present formulae to compute the cumulant generating function for general window functions.

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arXiv2015

Consistent Modified Gravity Analysis of Anisotropic Galaxy Clustering Using BOSS DR11

We analyse the clustering of cosmic large scale structure using a consistent modified gravity perturbation theory, accounting for anisotropic effects along and transverse to the line of sight. The growth factor has a particular scale dependence in f(R) gravity and we fit for the shape parameter f_{R0} simultaneously with the distance and the large scale (general relativity) limit of the growth function. Using more than 690,000 galaxies in the Baryon Oscillation Spectroscopy Survey Data Release 11, we find no evidence for extra scale dependence, with the 95\% confidence upper limit |f_{R0}| <8 \times 10^{-4}. Future clustering data, such as from the Dark Energy Spectroscopic Instrument, can use this consistent methodology to impose tighter constraints.

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arXiv2015

On the importance of nonlinear couplings in large-scale neutrino streams

We propose a procedure to evaluate the impact of nonlinear couplings on the evolution of massive neutrino streams in the context of large-scale structure growth. Such streams can be described by general nonlinear conservation equations, derived from a multiple-flow perspective, which generalize the conservation equations of non-relativistic pressureless fluids. The relevance of the nonlinear couplings is quantified with the help of the eikonal approximation applied to the subhorizon limit of this system. It highlights the role played by the relative displacements of different cosmic streams and it specifies, for each flow, the spatial scales at which the growth of structure is affected by nonlinear couplings. We found that, at redshift zero, such couplings can be significant for wavenumbers as small as $k=0.2\,h$/Mpc for most of the neutrino streams.

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