The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?

TL;DR

This study demonstrates that the cosmic shear likelihood is significantly non-Gaussian, which affects parameter estimates and suggests the low  value from the CDFS is not as unusual as previously thought.

Contribution

It provides the first detailed analysis of the non-Gaussianity of the cosmic shear likelihood and its impact on cosmological parameter estimation, especially for the CDFS data.

Findings

Cosmic shear likelihood is significantly non-Gaussian.

Re-analysis of CDFS data yields higher  values when accounting for non-Gaussianity.

Biases from CDFS selection can influence  estimates.

Abstract

(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of $\sigma_8$ really is as derived from the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account as well as the possibility of biases coming from the way the CDFS was selected. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood. Assuming that the CDFS is a random pointing, we find $\sigma_8=0.68_{-0.16}^{+0.09}$ for fixed $\Omega_{\rm m}=0.25$. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in $\approx 5%$ of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain $\sigma_8 = 0.71^{+0.10}_{-0.15}$. Combining the CDFS data with the parameter constraints from WMAP5 yields $\Omega_{\rm m} = 0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat universe.