The covariance of cosmic shear correlation functions and cosmological parameter estimates using redshift information

Institut für Astrophysik und Extraterrestrische Forschung, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

Corresponding author: P. Simon, psimon@astro.uni-bonn.de

Received: 1 September 2003
Accepted: 13 January 2004

Abstract

Cosmological weak lensing by the large scale structure of the Universe, cosmic shear, is coming of age as a powerful probe of the parameters describing the cosmological model and matter power spectrum. It complements Cosmic Microwave Background studies, by breaking degeneracies and providing a cross-check. Furthermore, upcoming cosmic shear surveys with photometric redshift information will enable the evolution of dark matter to be studied, and even a crude separation of sources into redshift bins leads to improved constraints on parameters. An important measure of the cosmic shear signal are the shear correlation functions; these can be directly calculated from data, and compared with theoretical expectations for different cosmological models and matter power spectra. We present a Monte Carlo method to quickly simulate mock cosmic shear surveys. One application of this method is in the determination of the full covariance matrix for the correlation functions; this includes redshift binning and is applicable to arbitrary survey geometries. Terms arising from shot noise and cosmic variance (dominant on small and large scales respectively) are accounted for naturally. As an illustration of the use of such covariance matrices, we consider to what degree confidence regions on parameters are tightened when redshift binning is employed. The parameters considered are those commonly discussed in cosmic shear analyses – the matter density parameter , dark energy density parameter (classical cosmological constant) , power spectrum normalisation and shape parameter Γ. We incorporate our covariance matrices into a likelihood treatment, and also use the Fisher formalism to explore a larger region of parameter space. Parameter uncertainties can be decreased by a factor of ∼4-8 (∼5-10) with 2 (4) redshift bins.