Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

TL;DR

This study demonstrates that a Gaussian likelihood provides accurate parameter constraints for upcoming Stage IV weak lensing surveys, even accounting for non-Gaussianities introduced by survey cut-sky effects.

Contribution

It shows that the Gaussian likelihood is sufficient for accurate cosmological parameter estimation from weak lensing power spectra, simplifying analysis for future surveys.

Findings

Gaussian likelihood yields accurate parameter constraints.

Cut-sky non-Gaussianity is insufficient to bias results.

Comparison with N-body simulations confirms negligible non-Gaussian effects.

Abstract

We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.