Finding the distribution of matter using lenses - II: deconvolution-based reconstruction with 3x2pt measurements

Abstract

We present a deconvolution-based framework for testing scale-dependent departures of the late-time matter power spectrum from a fiducial cosmological model using $3\times2$pt measurements. We introduce a free-form scale-dependent modulation $A(k)$ of the fiducial nonlinear matter power spectrum and construct the linear response of binned galaxy-clustering, galaxy-galaxy-lensing, and cosmic-shear spectra to the discretized modulation $A(k)$. The response is evaluated with full-sky, beyond-Limber kernels including density, redshift-space-distortion, gravitational-shear, and intrinsic-alignment contributions. We reconstruct $A(k)$ using a regularized modified Richardson-Lucy algorithm, with weak diffusion in $\ln k$ and selection of the minimum-$\chi^2$ solution along the iteration history. Using Rubin/LSST Year 10-like synthetic data, we find that oscillatory modulations with amplitudes $\gtrsim1\%$ can be recovered over $0.1\lesssim k\lesssim0.5\,{\rm Mpc}^{-1}$, provided the oscillation frequency $f\lesssim10$ on $\log_{10}[k/(0.2\,{\rm Mpc}^{-1})]$. We further introduce a posterior-weighted consistency statistic calibrated with posterior-predictive null mocks, thereby accounting for cosmological and nuisance-parameter uncertainties without relying on Wilks' theorem. The null case is consistent with $A(k)=1$, while a $1\%$ oscillatory modulation is detected at $\sim 2.6\sigma$. These results demonstrate the potential of regularized deconvolution as a model-independent consistency test of the matter power spectrum in future $3\times2$pt surveys.