Inhomogeneity-induced variance of cosmological parameters

Fakultät für Physik, Universität Bielefeld, Universitätsstrasse 25, 33615 Bielefeld, Germany
e-mail: wiegand@physik.uni-bielefeld.de; dschwarz@physik.uni-bielefeld.de

Received: 22 September 2011
Accepted: 21 November 2011

Abstract

Context. Modern cosmology relies on the assumption of large-scale isotropy and homogeneity of the Universe. However, locally the Universe is inhomogeneous and anisotropic. This raises the question of how local measurements (at the  ~10² Mpc scale) can be used to determine the global cosmological parameters (defined at the  ~10⁴ Mpc scale)?

Aims. We connect the questions of cosmological backreaction, cosmic averaging and the estimation of cosmological parameters and show how they relate to the problem of cosmic variance.

Methods. We used Buchert’s averaging formalism and determined a set of locally averaged cosmological parameters in the context of the flat Λ cold dark matter model. We calculated their ensemble means (i.e. their global value) and variances (i.e. their cosmic variance). We applied our results to typical survey geometries and focused on the study of the effects of local fluctuations of the curvature parameter.

Results. We show that in the context of standard cosmology at large scales (larger than the homogeneity scale and in the linear regime), the question of cosmological backreaction and averaging can be reformulated as the question of cosmic variance. The cosmic variance is found to be highest in the curvature parameter. We propose to use the observed variance of cosmological parameters to measure the growth factor.

Conclusions. Cosmological backreaction and averaging are real effects that have been measured already for a long time, e.g. by the fluctuations of the matter density contrast averaged over spheres of a certain radius. Backreaction and averaging effects from scales in the linear regime, as considered in this work, are shown to be important for the precise measurement of cosmological parameters.