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)], can be used to extract the baryonic acoustic oscillation 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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• Baryon acoustic oscillations
• Dark energy
• Dark matter
• Evolution of the Universe
• Large scale structure of the Universe