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

Free access article

Issue		A&A Volume 504, Number 3, September IV 2009


Page(s)		689 - 703
Section		Cosmology (including clusters of galaxies)
DOI		http://dx.doi.org/10.1051/0004-6361/200911697
Published online		09 July 2009

A&A 504, 689-703 (2009)
DOI: 10.1051/0004-6361/200911697

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

J. Hartlap¹, T. Schrabback^{2, 1}, P. Simon³, and P. Schneider¹

¹ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
e-mail: hartlap@astro.uni-bonn.de
² Leiden Observatory, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
³ The Scottish Universities Physics Alliance (SUPA), Institute for Astronomy, School of Physics, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK

Received 20 January 2009 / Accepted 19 June 2009

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 $\sigma_8$ 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 $\sigma_8=0.68_{-0.16}^{+0.09}$ 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.

Key words: gravitational lensing -- cosmology: cosmological parameters -- methods: statistical -- methods: numerical

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