arXiv subjects

Alexandre Barthelemy

Publications and source records attributed to Alexandre Barthelemy.

13 recordsLinked to original sources

arXiv2026

Lensing without mixing: Probing Baryonic Acoustic Oscillations and other scale-dependent features in cosmic shear surveys

Weak-gravitational lensing tends to wash out scale- and time-dependent features of the clustering of matter, such as the baryonic acoustic oscillations which appear in the form of wiggles in the matter power spectrum but that disappear in the analogous lensing $C_\ell$. This is a direct consequence of lensing being a projected effect. In this paper, we demonstrate how the noise complexity-often deemed "erasing the signal"-induced by a particular deprojection technique, the Bernardeau-Nishimichi-Taruya transform [Mon. Not. R. Astron. Soc. 445, 1526 (2014), arXiv:1312.0430], can be used to extract the BAO signal and non-Gaussian aperture-mass-like properties at chosen physical scales. We take into account parts of the data vectors that should effectively be without cosmological signature and also introduce an additional reweighting designed to specifically highlight clustering features-at both the probe (summary statistics) or map (amplitude of the field) level. We thus demonstrate why weak-gravitational lensing by the large-scale structure of the Universe, though only in a tomographic setting, does not erase scale- and time-dependent features of the dynamics of matter-while providing a tool to effectively extract them from actual galaxy-shape measurements.

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arXiv2025

Clustering of the extreme: A theoretical description of weak lensing critical points power spectra in the mildly nonlinear regime

In cosmic web analysis, complementary to traditional cosmological probes, the extrema (e.g. peaks and voids) two-point correlation functions (2PCFs) are of particular interest for the study of both astrophysical phenomena and cosmological structure formation. However most previous studies constructed those statistics via N-body simulations without a robust theoretical derivation from first principles. A strong motivation exists for analytically describing the 2PCFs of these local extrema, taking into account the nonlinear gravitational evolution in the late Universe. In this paper, we derive analytical formulae for the power spectra and 2PCFs of 2D critical points, including peaks (maxima), voids (minima) and saddle points, in mildly non-Gaussian weak gravitational lensing fields. We apply a perturbative bias expansion to model the clustering of 2D critical points. We successfully derive the power spectrum of weak lensing critical points up to the next-to-next-to-leading order (NNLO) in gravitational perturbation theory, where trispectrum configurations of the weak lensing field have to be included. We numerically evaluate those power spectra up to the next-to-leading order (NLO), which correspond to the inclusion of bispectrum configurations, and transform them to the corresponding 2PCFs. An exact Monte Carlo (MC) integration is performed assuming a Gaussian distributed density field to validate our theoretical predictions. Overall, we find similar properties in 2D compared to the clustering of 3D critical points previously measured from N-body simulations. Contrary to standard lensing power spectra analysis, we find distinct BAO features in the lensing peak 2PCFs due to the gradient and curvature constraints, and we quantify that non-Gaussianity makes for ~10% of the signal at quasi-linear scales which could be important for current stage-IV surveys.

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arXiv2024

Theoretical wavelet $\ell_1$-norm from one-point PDF prediction

Weak gravitational lensing, resulting from the bending of light due to the presence of matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It stands as a pivotal objective for upcoming surveys. In the realm of current and forthcoming full-sky weak-lensing surveys, the convergence maps, representing a line-of-sight integration of the matter density field up to the source redshift, facilitate field-level inference, providing an advantageous avenue for cosmological exploration. Traditional two-point statistics fall short of capturing non-Gaussianities, necessitating the use of higher-order statistics to extract this crucial information. Among the various higher-order statistics available, the wavelet $\ell_1$-norm has proven its efficiency in inferring cosmology (Ajani et al.2021). However, the lack of a robust theoretical framework mandates reliance on simulations, demanding substantial resources and time. Our novel approach introduces a theoretical prediction of the wavelet $\ell_1$-norm for weak lensing convergence maps, grounded in the principles of Large-Deviation theory. We present, for the first time, a theoretical prediction of the wavelet $\ell_1$-norm for convergence maps, derived from the theoretical prediction of their one-point probability distribution. Additionally, we explore the cosmological dependence of this prediction and validate the results on simulations. A comparison of our predicted wavelet $\ell_1$-norm with simulations demonstrates a high level of accuracy in the weakly non-linear regime. Moreover, we show its ability to capture cosmological dependence, paving the way for a more robust and efficient parameter inference process.

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arXiv2024

Unleashing cosmic shear information with the tomographic weak lensing PDF

In this work, we demonstrate the constraining power of the tomographic weak lensing convergence PDF for StageIV-like source galaxy redshift bins and shape noise. We focus on scales of $10$ to $20$ arcmin in the mildly nonlinear regime, where the convergence PDF and its changes with cosmological parameters can be predicted theoretically. We model the impact of reconstructing the convergence from the shear field using the well-known Kaiser-Squires formalism. We cross-validate the predicted and the measured convergence PDF derived from convergence maps reconstructed using simulated shear catalogues. Employing a Fisher forecast, we determine the constraining power for $(\Omega_{m},S_{8},w_{0})$. We find that adding a 5-bin tomography improves the $\kappa-$PDF constraints by a factor of $\{3.8,1.3,1.6\}$ for $(\Omega_{m}, S_{8},w_{0})$ respectively. Additionally, we perform a joint analysis with the shear two-point correlation functions, finding an enhancement of around a factor of $1.5$ on all parameters with respect to the two-point statistics alone. These improved constraints come from disentangling $\Omega_{\rm m}$ from $w_0$ by extracting non-Gaussian information, in particular, including the PDF skewness at different redshift bins. We also study the effect of varying the number of parameters to forecast, in particular we add $h$, finding that the convergence PDF maintains its constraining power while the precision from two-point correlations degrades by a factor of $\{1.7,1.4,1.8\}$ for $\{\Omega_{\rm m},S_8,w_0\}$, respectively.

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arXiv2024

Making the leap I: Modelling the reconstructed lensing convergence PDF from cosmic shear with survey masks and systematics

The last few years have seen the development of a promising theoretical framework for statistics of the cosmic large-scale structure -- the theory of large deviations (LDT) for modelling weak-lensing one-point statistics in the mildly non-linear regime. The goal of this series of papers is to make the leap and lay out the steps to perform an actual data analysis with this theoretical tool. Building upon the LDT framework, in this work (Paper I) we demonstrate how to accurately model the Probability Distribution Function (PDF) of a reconstructed Kaiser-Squires convergence field under a realistic mask, that of the third data release of the Dark Energy Survey (DES). We also present how weak lensing systematics and higher-order lensing corrections due to intrinsic alignments, shear biases, photo-$z$ errors and baryonic feedback can be incorporated in the modelling of the reconstructed convergence PDF. In an upcoming work (Paper II) we will then demonstrate the robustness of our modelling through simulated likelihood analyses, the final step required before applying our method to actual data.

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arXiv2023

A theoretical view of the T-web statistical description of the cosmic web

The classification of the cosmic web into different environments is both a tool to study in more detail the formation of halos and galaxies via the link between their properties and the large-scale environment and as a class of objects whose statistics contain cosmological information. In this paper, we present an analytical framework to compute the probability of the different environments in the cosmic web based on the T-web formalism that classifies structures in four different classes (voids, walls, filaments, knots) by studying the eigenvalues of the tidal tensor (Hessian of the gravitational potential). This method relies on studying the eigenvalues of the tidal tensor with respect to a given threshold and thus requires the knowledge of the JPDF of those eigenvalues. We perform a change of variables in terms of minimally correlated rotational invariants and we study their distribution in the linear regime of structure formation, and in the quasi-linear regime with the help of a Gram-Charlier expansion and tree-order Eulerian perturbation theory. This expansion allows us to predict the probability of the different environments in the density field at a given smoothing scale as a function of the chosen threshold and redshift. We check the validity of our predictions by comparing those predictions to measurements made in the N-body Quijote simulations. We notably find that scaling the threshold value with the non-linear amplitude of fluctuations allows us to capture almost entirely the redshift evolution of the probability of the environments, even if we assume that the density field is Gaussian (corresponding to the linear regime of structure formation). We also show that adding mild non-Gaussian corrections in the form of third-order cumulants of the field provides even more precise predictions for cosmic web abundances up to scales as small as ~5 Mpc/h and redshifts down to z~0.

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arXiv2023

The cumulant generating function as a novel observable to cumulate weak lensing information

Key non-Gaussian properties of cosmological fields can be captured by their one-point statistics, providing a complement to two-point statistical measurements from power spectra or correlation functions. Large deviation theory can robustly predict the one-point statistics of cosmological density fields on mildly non-linear scales from first principles. It provides a direct prediction for the cumulant generating function (CGF) of such fields, from which a prediction for the more commonly used probability density function (PDF) is extracted through an inverse Laplace transform. For joint one-point statistics of multiple fields, the inverse Laplace transform rapidly becomes more cumbersome and computationally expensive. In this work, we demonstrate for the first time that the weak lensing CGF itself can be used as an observable that captures an equal amount of cosmological information to the PDF. While we use the weak-lensing convergence field as a simplistic and instructive example, this work is intended as a first step towards a cosmological analysis based on large deviation theory in the context of a nulling framework, which excludes contributions from small scales to facilitate highly accurate theoretical predictions. In this context, the method should be generally applicable for a multi-scale tomographic analysis of weak lensing and galaxy clustering.

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arXiv2023

It takes two to know one: Computing accurate one-point PDF covariances from effective two-point PDF models

One-point probability distribution functions (PDFs) of the cosmic matter density are powerful cosmological probes that extract non-Gaussian properties of the matter distribution and complement two-point statistics. Computing the covariance of one-point PDFs is key for building a robust galaxy survey analysis for upcoming surveys like Euclid and the Rubin Observatory LSST and requires good models for the two-point PDFs characterising spatial correlations. In this work, we obtain accurate PDF covariances using effective shifted lognormal two-point PDF models for the mildly non-Gaussian weak lensing convergence and validate our predictions against large sets of Gaussian and non-Gaussian maps. We show how the dominant effects in the covariance matrix capturing super-sample covariance arise from a large-separation expansion of the two-point PDF and discuss differences between the covariances obtained from small patches and full sky maps. Finally, we describe how our formalism can be extended to characterise the PDF covariance for 3D-dimensional spectroscopic fields using the 3D matter PDF as an example. We describe how covariances from simulated boxes with fixed overall density can be supplemented with the missing super-sample covariance effect by relying on theoretical predictions validated against separate-universe style simulations.

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arXiv2022

Numerical complexity of the joint nulled weak-lensing probability distribution function

In the context of tomographic cosmic shear surveys, there exists a nulling transformation of weak lensing observations (also called BNT transform) that allows us to simplify the correlation structure of tomographic cosmic shear observations, as well as to build observables that depend only on a localised range of redshifts and thus independent from the low-redshift/small-scale modes. This procedure renders possible accurate, and from-first-principles, predictions of the convergence and aperture mass one-point distributions (PDF). We here explore other consequences of this transformation on the (reduced) numerical complexity of the estimation of the joint PDF between nulled bins and demonstrate how to use these results to make theoretical predictions.

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arXiv2021

Nuw CDM cosmology from the weak lensing convergence PDF

Pinning down the total neutrino mass and the dark energy equation of state is a key aim for upcoming galaxy surveys. Weak lensing is a unique probe of the total matter distribution whose non-Gaussian statistics can be quantified by the one-point probability distribution function (PDF) of the lensing convergence. We calculate the convergence PDF on mildly non-linear scales from first principles using large-deviation statistics, accounting for dark energy and the total neutrino mass. For the first time, we comprehensively validate the cosmology-dependence of the convergence PDF model against large suites of simulated lensing maps, demonstrating its percent-level precision and accuracy. We show that fast simulation codes can provide highly accurate covariance matrices, which can be combined with the theoretical PDF model to perform forecasts and eliminate the need for relying on expensive N-body simulations. Our theoretical model allows us to perform the first forecast for the convergence PDF that varies the full set of $Λ$CDM parameters. Our Fisher forecasts establish that the constraining power of the convergence PDF compares favourably to the two-point correlation function for a Euclid-like survey area at a single source redshift. When combined with a CMB prior from Planck, the PDF constrains both the neutrino mass $M_ν$ and the dark energy equation of state $w_0$ more strongly than the two-point correlation function.

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arXiv2021

Probability distribution function of the aperture mass field with large deviation theory

In the context of tomographic cosmic shear surveys, a theoretical model for the one-point statistics of the aperture mass (Map) is developed. This formalism is based on the application of the large deviation principle to the projected matter density field and more specifically to the angular aperture masses. The latter holds the advantage of being an observable that can be directly extracted from the observed shear field and to be, by construction, independent from the long wave modes. Furthermore we show that, with the help of a nulling procedure based on the so-called BNT transform, it is possible to build observables that depend only on a finite range of redshifts making them also independent from the small-scale modes. This procedure makes predictions for the shape of the one-point Probability Distribution Function of such an observable very accurate, comparable to what had been previously obtained for 3D observables. Comparisons with specific simulations reveal however inconsistent results showing that synthetic lensing maps were not accurate enough for such refined observables. It points to the need for more precise dedicated numerical developments whose performances could be benchmarked with such observables. We furthermore review the possible systematics that could affect such a formalism in future weak-lensing surveys like Euclid, notably the impact of shape noise as well as leading corrections coming from lens-lens couplings, geodesic deviation, reduced shear and magnification bias.

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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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