Map-based cosmology inference with lognormal cosmic shear maps

Most cosmic shear analyses to date have relied on summary statistics (e.g. $\xi_+$ and $\xi_-$). These types of analyses are necessarily sub-optimal, as the use of summary statistics is lossy. In this paper, we forward-model the convergence field of the Universe as a lognormal random field conditioned on the observed shear data. This new map-based inference framework enables us to recover the joint posterior of the cosmological parameters and the convergence field of the Universe. Our analysis properly accounts for the covariance in the mass maps across tomographic bins, which significantly improves the fidelity of the maps relative to single-bin reconstructions. We verify that applying our inference pipeline to Gaussian random fields recovers posteriors that are in excellent agreement with their analytical counterparts. At the resolution of our maps -- and to the extent that the convergence field can be described by the lognormal model -- our map posteriors allow us to reconstruct \it all \rm summary statistics (including non-Gaussian statistics). We forecast that a map-based inference analysis of LSST-Y10 data can improve cosmological constraints in the $\sigma_8$--$\Omega_{\rm m}$ plane by $\approx 30\%$ relative to the currently standard cosmic shear analysis. This improvement happens almost entirely along the $S_8=\sigma_8\Omega_{\rm m}^{1/2}$ directions, meaning map-based inference fails to significantly improve constraints on $S_8$.