Euclid: Covariance of weak lensing pseudo-$C_\ell$ estimates. Calculation, comparison to simulations, and dependence on survey geometry

TL;DR

This paper thoroughly analyzes the covariance of pseudo-$C_\ell$ estimates in cosmic shear studies, comparing theoretical calculations with simulations, and highlights the importance of non-Gaussian contributions for accurate cosmological parameter estimation.

Contribution

It provides a detailed calculation and comparison of the covariance matrix, including mode-coupling effects, for different survey geometries, emphasizing the significance of non-Gaussian terms.

Findings

Good agreement between theory and simulations for covariance.

Increased sky cuts lead to larger covariance, especially non-Gaussian parts.

Neglecting non-Gaussian covariance underestimates uncertainties by up to 70%.

Abstract

An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-$C_\ell$ estimates of tomographic cosmic shear power spectra. Using two existing publicly available codes in combination, we calculate the full covariance matrix, including mode-coupling contributions arising from both partial sky coverage and non-linear structure growth. For three different sky masks, we compare the theoretical covariance matrix to that estimated from publicly available N-body weak lensing simulations, finding good agreement. We find that as a more extreme sky cut is applied, a corresponding increase in both Gaussian off-diagonal covariance and non-Gaussian super-sample covariance is observed in both theory and simulations, in accordance with expectations. Studying the different contributions to the covariance in detail, we find that the Gaussian covariance dominates along the main diagonal and the closest off-diagonals, but further away from the main diagonal the super-sample covariance is dominant. Forming mock constraints in parameters describing matter clustering and dark energy, we find that neglecting non-Gaussian contributions to the covariance can lead to underestimating the true size of confidence regions by up to 70 per cent. The dominant non-Gaussian covariance component is the super-sample covariance, but neglecting the smaller connected non-Gaussian covariance can still lead to the underestimation of uncertainties by 10--20 per cent. A real cosmological analysis will require marginalisation over many nuisance parameters, which will decrease the relative importance of all cosmological contributions to the covariance, so these values should be taken as upper limits on the importance of each component.