paper

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

arXiv:astro-ph/0309032 · doi:10.1051/0004-6361:20034251

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 CMB studies, by breaking degeneracies and providing a cross-check. 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. We incorporate our covariance matrices into a likelihood treatment, and also use the Fisher formalism to explore a larger region of parameter space (abridged).

arXiv comment14 pages, 8 figures, accepted by A&A corrected typos, some changes in the discussion, shortened sections 2.1, 2.2 and 6.2.1

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