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 (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.

💡 Research Summary

The paper addresses a long‑standing limitation of weak‑gravitational lensing (WL) as a cosmological probe: because WL measures the integrated effect of the three‑dimensional matter distribution along the line of sight, scale‑dependent features such as the Baryon Acoustic Oscillations (BAO) are heavily “washed out” in the usual angular power spectrum Cℓ. The authors demonstrate that this apparent loss of information is not fundamental, and can be overcome by applying the Bernardeau‑Nishimichi‑Taruya (BNT) transform, a linear re‑weighting of tomographic shear maps that isolates specific physical lensing distances.

The BNT transform works by constructing a matrix p that acts on the set of tomographic source bins. For each consecutive triplet of bins, the matrix elements are fixed by the condition that the transformed lensing efficiency kernels ˆωa have zero contribution from lenses below a chosen comoving distance. This “nulling” of low‑redshift lenses is achieved analytically using the inverse‑weighted comoving distance X_i defined in the paper. The resulting kernels are sharply localized in redshift, allowing a clean mapping between angular multipole ℓ and three‑dimensional wavenumber k.

Armed with these localized kernels, the authors split the linear matter power spectrum into a smooth “no‑wiggle” component P_nw(k) and an oscillatory BAO component P_w(k). They introduce two phenomenological parameters: the BAO amplitude A (relative to the fiducial wiggles) and a shift ks that moves the wiggle positions. Using the transformed convergence power spectra Ĉκ̂κab(ℓ) for all bin pairs (a,b), they build a data vector that also includes a shape‑noise term scaled by a nuisance amplitude α. The covariance is modeled with the standard Gaussian Knox approximation, including both cosmic variance and shape noise.

A Fisher‑matrix analysis is performed, marginalizing over α, and two different choices of data vector are compared. The first uses only the “non‑null” correlators (|a‑b|≤2) that have non‑zero cosmological expectation values; the second uses the full set of correlators, including those whose expectation value is exactly zero after the BNT transform. Surprisingly, the full data vector yields a factor ≈4 improvement in the figure of merit for (A, ks). The authors explain this by noting that the BNT transform diagonalizes the cosmological signal covariance while simultaneously making the noise covariance highly non‑diagonal. The “null” correlators, though signal‑free, carry detailed information about the noise structure, allowing a much tighter constraint on α and consequently on the cosmological parameters.

The authors also exploit the clean ℓ‑k mapping to apply a physical k‑cut, retaining only modes in the range 4×10⁻³ ≤ k ≤ 4×10⁻¹ h Mpc⁻¹, which encompasses the BAO scales while discarding poorly modeled non‑linear regimes. Under Euclid‑like survey specifications (sky fraction f_sky = 0.36, galaxy densities of 30 and 60 gal arcmin⁻², realistic photometric redshift errors, and Gaussian shape noise), the Fisher forecasts show that the no‑wiggle model (A=0) can be excluded at the 1σ level for 30 gal arcmin⁻² and at the 4σ level for 60 gal arcmin⁻² when the full data vector is used. This demonstrates that pure cosmic‑shear measurements, without any galaxy‑clustering cross‑correlations, can independently recover BAO information.

Beyond the two‑point function, the paper argues that the BNT transform also facilitates the extraction of non‑Gaussian, aperture‑mass‑like statistics at chosen physical scales, because the same localized kernels can be applied to map‑level quantities. The authors discuss possible extensions to incorporate non‑linear growth models, baryonic feedback, and higher‑order statistics such as the bispectrum, suggesting that the BNT framework could become a versatile tool for Stage‑IV lensing surveys (Euclid, LSST, Roman).

In summary, the study overturns the conventional belief that weak lensing cannot probe BAO. By leveraging the BNT nulling transform, carefully accounting for the altered noise covariance, and employing a physical k‑cut, the authors show that BAO wiggles can be detected with competitive significance using only shear‑shear correlations. This opens a new avenue for combining lensing‑only BAO measurements with traditional galaxy‑clustering BAO, potentially tightening constraints on dark energy, curvature, and the physics of the early Universe.