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

TL;DR

This work shows that weak lensing, traditionally limited by line-of-sight projection, can reveal scale- and time-dependent features such as BAO by applying the Bernardeau-Nishimichi-Taruya (BNT) transform to cosmic shear data. By narrowing lensing kernels into effective, reweighted efficiencies $\hat{\omega}_a$, the authors recover BAO wiggles in both the lensing power spectra and the corresponding two-point function, and they demonstrate probe- and field-level reconstructions that map transformed observables back toward the underlying three-dimensional matter field. A key finding is that correlators with vanishing cosmological expectation still carry meaningful information about noise covariance, and incorporating them substantially improves BAO constraints (by up to a factor of ~4 in their Fisher analysis). They further develop a formal framework to reconstruct higher-order cumulants via Limber-Approximated geometry, culminating in a field-level cumulant generating functional and an illustrative reconstruction of the matter skewness, with non-linear growth incorporated through a generalized $D_{+,\mathrm{nl}}$. Overall, the BNT approach enables a principled, scale-localized interpretation of cosmic shear data and opens pathways to observing BAO and other scale-dependent features directly from tomographic lensing surveys like Euclid.

Abstract

Weak-gravitational lensing tends to wash out scale and time-dependent features of the clustering of matter, such as the Baryonic Acoustic Oscillations (BAO) 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 de-projection technique, the Bernardeau-Nishimichi-Taruya (BNT) transform 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 re-weighting designed to specifically highlight clustering features -- both at 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-shapes measurements.

Figures (11)

• Figure 1: Lensing efficiency kernels for 10 equally populated redshift bins of our semi-realistic Euclid-like distribution of sources, prior to nulling (dashed lines) and after nulling (thick lines). The bottom plot shows the shape of the normalized distribution of sources inside each bin. They follow equation \ref{['eq:n_iz']}.
• Figure 2: Constraints at $1 \sigma$ obtained with Fisher analysis for the two BAO parameters with a total galaxy number density of $30 {\rm gal/arcmin^2}$ and $60 {\rm gal/arcmin^2}$, those values can be found in Euclid:2025plmEuclid:2025vsf. $A$ is the relative amplitude of the wiggles and $k_{\rm shift}$ [${\rm Mpc}^{-1}$] a shift of their position in the matter power spectrum. We compare the results taking the full data vector and only correlators such that $|a-b| \leq 2$.
• Figure 3: BNT Transformed Correlation Matrix at $\ell=100$. Elements are ordered per distance between indices. Green lines divide each axis between elements of the data vector of null and non-null expectation values, with two categories of null elements as described in the main text.
• Figure 4: Comparison of probe-level effective power spectra and their real-space counterpart from auto bin lensing correlations.
• Figure 5: Comparison of real-space effective correlation functions reconstructed using the two different definitions for $\chi_{{\rm eff},a}$ and $\sigma^2_{\chi,a}$ in equation \ref{['eq:omega_bnt_eff']}. Each plot shows bin auto-correlations and their average, along with the matter two-point function in linear and nonlinear theory.