Analysis of two-point statistics of cosmic shear: I. Estimators and covariances

TL;DR

This paper derives covariance matrices for cosmic shear two-point statistics, introduces estimators for the power spectrum, and assesses their impact on cosmological parameter estimation accuracy.

Contribution

It provides new expressions for covariance matrices applicable to any survey geometry and introduces estimators for the power spectrum with weak inter-band correlations.

Findings

A simple survey geometry approximation for covariance matrices.

A rapid decorrelation of aperture mass dispersion at different scales.

Cosmic shear can precisely estimate key cosmological parameters.

Abstract

We derive in this paper expressions for the covariance matrix of the cosmic shear two-point correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry which allows us to obtain approximations for the covariance matrix in terms of integrals which are readily evaluated numerically. These results are then used to study the covariance of the aperture mass dispersion which has been employed earlier in quantitative cosmic shear analyses. We show that the aperture mass dispersion, measured at two different angular scales, quickly decorrelates with the ratio of the scales. Inverting the relation between the shear two-point correlation functions and the power spectrum of the underlying projected matter distribution, we construct estimators for the power spectrum and for the band powers, and show that they yields accurate approximations; in particular, the correlation between band powers at different wave numbers is quite weak. The covariance matrix of the shear correlation function is then used to investigate the expected accuracy of cosmological parameter estimates from cosmic shear surveys. Depending on the use of prior information, e.g. from CMB measurements, cosmic shear can yield very accurate determinations of several cosmological parameters, in particular the normalization $\sigma_8$ of the power spectrum of the matter distribution, the matter density parameter $\Omega_{\rm m}$, and the shape parameter $\Gamma$.