Almanac: Weak Lensing power spectra and map inference on the masked sphere

TL;DR

This paper introduces a Bayesian method for extracting weak lensing power spectra and maps from noisy, masked sky observations, enabling detailed cosmological analysis including non-gaussianity and parity-violation.

Contribution

It presents a novel field-based Bayesian inference framework for jointly estimating weak lensing power spectra and maps on the masked sphere using Hamiltonian Monte Carlo sampling.

Findings

Successfully infers all-sky E- and B-mode power spectra up to rac{}{}max=2048

Produces noise-cleaned shear and convergence maps for cosmological analysis

Handles complex masks and noise levels similar to Euclid-like surveys

Abstract

We present a field-based signal extraction of weak lensing from noisy observations on the curved and masked sky. We test the analysis on a simulated Euclid-like survey, using a Euclid-like mask and noise level. To make optimal use of the information available in such a galaxy survey, we present a Bayesian method for inferring the angular power spectra of the weak lensing fields, together with an inference of the noise-cleaned tomographic weak lensing shear and convergence (projected mass) maps. The latter can be used for field-level inference with the aim of extracting cosmological parameter information including non-gaussianity of cosmic fields. We jointly infer all-sky $E$-mode and $B$-mode tomographic auto- and cross-power spectra from the masked sky, and potentially parity-violating $EB$-mode power spectra, up to a maximum multipole of $\ell_{\rm max}=2048$. We use Hamiltonian Monte Carlo sampling, inferring simultaneously the power spectra and denoised maps with a total of $\sim 16.8$ million free parameters. The main output and natural outcome is the set of samples of the posterior, which does not suffer from leakage of power from $E$ to $B$ unless reduced to point estimates. However, such point estimates of the power spectra, the mean and most likely maps, and their variances and covariances, can be computed if desired.