arXiv subjects

Francis Bernardeau

Publications and source records attributed to Francis Bernardeau.

At least 19 recordsLinked to original sources

arXiv2026

KiDS-Legacy: The consistency test of the large-scale structure with Bernardeau-Nishimichi-Taruya transform

We perform the first $k$-cut cosmic shear analysis of the KiDS-Legacy survey. This method uses the Bernardeau-Nishimichi-Taruya (BNT) transform to construct weak-lensing kernels that are more localised than conventional ones, and remove information from selected physical scales while retaining the constraining power of the targeted range. Removing the scale of $k \geq 0.33~\mathrm{Mpc}^{-1}$ from the KiDS-Legacy pseudo-$C_\ell$ data vector, and using a covariance matrix whose Gaussian component is computed from the theoretical data vector, we find $S_8 = 0.798 \pm 0.045$. This agrees with both the fiducial KiDS-Legacy bandpower result and our no-$k$-cut pseudo-$C_\ell$ posterior to within $0.1\sigma$, indicating no significant bias from nonlinear astrophysical feedback at the precision of KiDS-Legacy. We also study the case in which the Gaussian covariance is computed from the observed data vector. In this setup, the same scale cut of $k < 0.33~\mathrm{Mpc}^{-1}$ gives a much lower $S_8=0.717_{-0.046}^{+0.047}$. Further $k$-cut tests reveal a mild scale-dependent trend, with larger physical scales preferring lower $S_8$ values and a maximum low- versus high-$k$ deviation of $1.80\sigma$. Mock tests show that this behaviour is not produced by the covariance prescription or data vector alone, but may arise from their interplay. These results show that BNT $k$-cuts provide both a mitigation strategy for nonlinear systematics and a diagnostic of weak-lensing inference pipelines.

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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

Mitigating Nonlinear Systematics in Weak Lensing Surveys II: Stability and Diagnostics with Intrinsic Alignment

The Bernardeau-Nishimichi-Taruya (BNT) transform provides a powerful framework for analysing tomographic cosmic shear data by improving the localization of shear correlations in physical scale. It operates by performing a linear combination of the shear data vector in $\ell$-space, yielding a transformed vector that is better localized in both redshift and $k$-space. BNT is particularly useful for estimating cosmological parameters while minimizing the impact of poorly understood nonlinear physics, without discarding large amounts of information as is typically done with simple scale cuts. In our previous work, we showed that BNT outperforms traditional weak-lensing analyses; however, that study did not include intrinsic alignments (IA). In the present work, we assess the robustness of our BNT-based $k$-cut framework in the presence of realistic IA models. We consider two cases: (i) when the assumed IA model used in sampling is close to, but not identical to, the true one, and (ii) when the assumed IA model is significantly biased compared to the true one. In the first case, the $k$-cut framework yields precise and unbiased $S_8$ constraints even with limited knowledge of large-scale modes. Using Euclid-like mock data and a stringent $k$-cut of $k \le 0.1\;{\rm Mpc^{-1}}$ for all tomographic bins, we found that BNT can constrain $S_8$ with a precision better than 2\% while non-BNT has lost all constraining power. In the second case, the BNT transform serves as a powerful diagnostic tool, revealing internal inconsistencies in $k$-space and redshift-space both exceeding 5$\sigma$ when the functional form of the sampling and fiducial IA models differ fundamentally.

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arXiv2025

The Topology of Rayleigh-Levy Flights in Two Dimensions

Rayleigh-L\'evy flights are simplified cosmological tools which capture certain essential statistical properties of the cosmic density field, including hierarchical structures in higher-order correlations, making them a valuable reference for studying the highly non-linear regime of structure formation. Unlike standard Markovian processes, they exhibit long-range correlations at all orders. Following on recent work on one dimensional flights, this study explores the one-point statistics and Minkowski functionals (density PDF, perimeter, Euler characteristic) of Rayleigh-L\'evy flights in two dimensions. We derive the Euler characteristic in the mean field approximation and the density PDF and iso-field perimeter $W_{1}$ in beyond mean field calculations, and validate the results against simulations. The match is excellent throughout, even for fields with large variances, in particular when finite volume effects in the simulations are taken into account and when the calculation is extended beyond the mean field.

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arXiv2025

Novel geometrical test of cosmological expansion from photometric data

In tomographic cosmic-shear observations, the BNT (Bernardeau, Nishimichi, Taruya) transform, Bernardeau et al. (2014), allows to build weak lensing transformed maps for which the contribution from low redshift lenses is nulled. As this transformation depends specifically on the expansion rate of the Universe but is independent of the matter distribution properties, it can be leveraged to extract information from large-scale structure probes at arbitrary non-linear scales, providing constraints on cosmological background evolution. We demonstrate this by proposing a specific null test for stage IV weak lensing projects. Using a Fisher matrix analysis and parameter sampling, we show that this approach can substantially enhance constraints on the dark energy equation of state. Notably, we find that shape noise currently limits this method's effectiveness making significant improvement possible in future designs. A detailed analysis of our null test in the context of the Euclid mission is presented in a companion paper Touzeau et al. (2025).

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arXiv2025

Cosmic shear nulling as a geometrical cosmological probe: Methodology and sensitivity to cosmological parameters and systematics

Tomographic weak lensing surveys contain intrinsic symmetries that depend solely on the geometric structure of the Universe. These symmetries can be revealed through null tests and verifying their validity provides constraints on cosmological parameters that govern the background evolution-particularly the redshift dependence of the angular diameter distance. This forms the foundation of the tomographic cosmic shear nulling test introduced in this work. We describe how this test can be implemented, what aspects of cosmology it can constrain, and its specific efficiency in doing so. We also assess its sensitivity to astrophysical effects-such as magnification bias and reduced shear corrections-as well as to observational systematics, including errors in the mean redshift of source bins. Our results show that, in a survey configuration comparable to that of Euclid, this null test can yield complementary constraints on key cosmological parameters such as ${\Omega_{\rm m}, {\rm w}_0}$. However, due to its subdominant constraining power compared to standard 3x2pt analysis and through the identification of a required precision of order $10^{-3}$ on the mean redshift of the bins, we conclude that nulling would better be used as a photometric redshift calibration probe or consistency check. In combination with standard weak lensing and galaxy clustering analysis, it would then offer a promising route to better control systematics and improve the precision of future cosmological measurements.

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arXiv2024

Mitigating Nonlinear Systematics in Weak Lensing Surveys: The Bernardeau-Nishimichi-Taruya Approach

Weak lensing surveys, along with most other late-Universe probes, have consistently measured a lower amplitude of the matter fluctuation spectrum, denoted by the parameter $S_8$, compared to predictions from early-Universe measurements in cosmic microwave background data. Improper modelling of nonlinear scales may partially explain these discrepancies in lensing surveys. This study investigates whether the conventional approach to addressing small-scale biases remains optimal for Stage-IV lensing surveys. We demonstrate that conventional weak lensing estimators are affected by scale leakage from theoretical biases at nonlinear scales, which influence all observed scales. Using the BNT transform, we propose an $\ell$-cut methodology that effectively controls this leakage. The Bernardeau-Nishimichi-Taruya (BNT) transform reorganises weak lensing data in $\ell$ space, aligning it with $k$ space, thereby reducing the mixing of nonlinear scales and providing a more accurate interpretation of the data. We evaluate the BNT approach by comparing HMcode, Halofit, Baryon Correction Model and AxionHMcode mass power spectrum models using Euclid-like survey configurations. Additionally, we introduce a new estimator to quantify scale leakage in both the BNT and noBNT approaches. Our findings show that BNT outperforms traditional methods, preserving cosmological constraints while significantly mitigating theoretical biases.

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arXiv2024

The statistics of Rayleigh-Levy flight extrema

Rayleigh-Levy flights have played a significant role in cosmology as simplified models for understanding how matter distributes itself under gravitational influence. These models also exhibit numerous remarkable properties that enable the prediction of a wide range of characteristics. Here, we derive the one and two point statistics of extreme points within Rayleigh-Levy flights spanning one to three dimensions, stemming directly from fundamental principles. In the context of the mean field limit, we provide straightforward closed-form expressions for Euler counts and their correlations, particularly in relation to their clustering behaviour over long distances. Additionally, quadratures allow for the computation of extreme value number densities. A comparison between theoretical predictions in 1D and Monte Carlo measurements shows remarkable agreement. Given the widespread use of Rayleigh-Levy processes, these comprehensive findings offer significant promise not only in astrophysics but also in broader applications beyond the field.

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arXiv2023

Perturbation theory challenge for cosmological parameters estimation II.: Matter power spectrum in redshift space

Constraining cosmological parameters from large-scale structure observations requires precise and accurate tools to compute its properties. While perturbation theory (PT) approaches can serve this purpose, exploration of large parameter space is challenging due to the potentially large computational cost of such calculations. In this study, we show that a response function approach applied to the regularized PT (RegPT) model at 2-loop order, plus correction terms induced by redshift space distortion effects, can reduce the runtime by a factor of 50 compared to direct integration. We illustrate the performance of this approach by performing the parameter inference of five fundamental cosmological parameters from the redshift space power spectrum measured from $N$-body simulations as mock measurements, and inferred cosmological parameters are directly compared with parameters used to generate initial conditions of the simulations. From this \textit{PT challenge} analysis, the constraining power of cosmological parameters and parameter biases are quantified with the survey volume and galaxy number density expected for the \textit{Euclid} mission at the redshift $z = 1$ as a function of the maximum wave-number of data points $k_\mathrm{max}$. We find that RegPT with correction terms reproduces the input cosmological parameters without bias up to maximum wave-number $k_\mathrm{max}= 0.18 \, h\,\mathrm{Mpc}^{-1}$. Moreover, RegPT+, which introduces one free parameter to RegPT to handle the damping feature on small scales, delivers the best performance among the examined models and achieves tighter constraints without significant parameter bias for higher maximum wave-number $k_\mathrm{max} = 0.21 \, h\,\mathrm{Mpc}^{-1}$.

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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

Covariances of density probability distribution functions. Lessons from hierarchical models

Context: Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF). In order to successfully exploit such observables, a detailed functional form of the covariance matrix of the one-point PDF is needed. Aims: The objectives are to model the properties of this covariance for general stochastic density fields in a cosmological context. Methods: Leading and subleading contributions to the covariance were identified within a large class of models, the so-called hierarchical models. The validity of the proposed forms for the covariance matrix was assessed with the help of a toy model, the minimum tree model, for which a corpus of exact results could be obtained (forms of the one- and two-point PDF, large-scale density-bias functions, and full covariance matrix of the one-point PDF). Results: It is first shown that the covariance matrix elements are directly related to the spatial average of the two-point density PDF within the sample. The dominant contribution to this average is explicitly given for hierarchical models, which leads to the construction of specific density-bias functions. However, this contribution alone cannot be used to construct an operational likelihood function. Short distance effects are found to be have an important impact but are more difficult to derive as they depend more on the details of the model. However, a simple and generic form of these contributions is proposed. Detailed comparisons in the context of the Rayleigh-Levy flight model show that the large-scale effects capture the bulk of the supersample effects and that, by adding the short-distance contributions, a qualitatively correct model of the likelihood function can be obtained.

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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

Implementing spectra response function approaches for fast calculation of power spectra and bispectra

Perturbation theory of large-scale structures of the Universe at next-to-leading order and next-to-next-to-leading order provides us with predictions of cosmological statistics at sub-percent level in the mildly non-linear regime. Its use to infer cosmological parameters from spectroscopic surveys, however, is hampered by the computational cost of making predictions for a large number of parameters. In order to reduce the running time of the codes, we present a fast scheme in the context of the regularized perturbation theory approach and applied it to power spectra at 2-loop level and bispectra at 1-loop level, including the impact of binning. This method utilizes a Taylor expansion of the power spectrum as a functional of the linear power spectrum around fiducial points at which costly direct evaluation of perturbative diagrams is performed and tabulated. The computation of the predicted spectra for arbitrary cosmological parameters then requires only one-dimensional integrals that can be done within a few minutes. It makes this method suitable for Markov chain Monte-Carlo analyses for cosmological parameter inference.

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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

x-cut Cosmic Shear: Optimally Removing Sensitivity to Baryonic and Nonlinear Physics with an Application to the Dark Energy Survey Year 1 Shear Data

We present a new method, called $x$-cut cosmic shear, which optimally removes sensitivity to poorly modeled scales from the two-point cosmic shear signal. We show that the $x$-cut cosmic shear covariance matrix can be computed from the correlation function covariance matrix in a few minutes, enabling a likelihood analysis at virtually no additional computational cost. Further we show how to generalize $x$-cut cosmic shear to galaxy-galaxy lensing. Performing an $x$-cut cosmic shear analysis of the Dark Energy Survey Year 1 (DESY1) shear data, we reduce the error on $S_8= σ_8 (Ω_m / 0.3) ^ {0.5}$ by $32 \%$ relative to a correlation function analysis with the same priors and angular scale cut criterion, while showing our constraints are robust to different baryonic feedback models. Largely driven by information at small angular scales, our result, $S_8= 0.734 \pm 0.026$, yields a $2.6 σ$ tension with the Planck Legacy analysis of the cosmic microwave background. As well as alleviating baryonic modelling uncertainties, our method can be used to optimally constrain a large number of theories of modified gravity where computational limitations make it infeasible to model the power spectrum down to extremely small scales. The key parts of our code are made publicly available.

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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

Power spectrum response of large-scale structure in 1D and in 3D: tests of prescriptions for post-collapse dynamics

The power spectrum response function of the large-scale structure of the Universe describes how the evolved power spectrum is modified by a small change in initial power through non-linear mode coupling of gravitational evolution. It was previously found that the response function for the coupling from small to large scales is strongly suppressed in amplitude, especially at late times, compared to predictions from perturbation theory (PT) based on the single-stream approximation. One obvious explanation for this is that PT fails to describe the dynamics beyond shell-crossing. We test this idea by comparing measurements in $N$-body simulations to prescriptions based on PT but augmented with adaptive smoothing to account for the formation of non-linear structures of various sizes in the multi-stream regime. We first start with one-dimensional (1D) cosmology, where the Zel'dovich approximation provides the exact solution in the single stream regime. Similarly to the 3D case, the response function of the large-scale modes exhibits a strong suppression in amplitude at small scales which cannot be explained by the Zel'dovich solution alone. However, by performing adaptive smoothing of initial conditions to identify haloes of different sizes and solving approximately post-collapse dynamics in the 3-streams regime, agreement between theory and simulations drastically improves. We extend our analyses to the 3D case using PINOCCHIO algorithm, in which similar adaptive smoothing is implemented on the Lagrangian PT fields to identify haloes and is combined with a spherical halo prescription to account for post-collapse dynamics. Again, a suppression is found in the coupling between small- and large-scale modes and the agreement with simulations is improved.

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arXiv2020

Observing Baryonic Acoustic Oscillations in tomographic cosmic shear surveys

We show that it is possible to build effective matter density power spectra in tomographic cosmic shear observations that exhibit the Baryonic Acoustic Oscillations (BAO) features once a nulling transformation has been applied to the data. The precision with which the amplitude and position of these features can be reconstructed is quantified in terms of sky coverage, intrinsic shape noise, median source redshift and number density of sources. BAO detection in Euclid or LSST like wide surveys will be possible with a modest signal-to-noise ratio. It would improve dramatically for slightly deeper surveys.

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