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

Abstract

Aims.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 σ8 really is as derived from the 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. Methods. A brute force approach to estimating the likelihood from simulations must fail because of the high dimensionality of the problem. We therefore use independent component analysis to transform the cosmic shear correlation functions to a new basis, in which the likelihood approximately factorises into a product of one-dimensional distributions. Results.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 in combination with conservative galaxy selection criteria that minimise calibration uncertainties. Assuming that the CDFS is a random pointing, we find σ8 = 0.68+0.09-0.16 for fixed Ωm = 0.25. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in ≈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 σ8 = 0.71+0.10 .0.15. Combining the CDFS data with the parameter constraints from WMAP5 yields Ωm = 0.26+0.03 .0.02 and σ8 = 0.79+0.04 .0.03 for a flat universe. © 2009 ESO.