Inhomogeneity-induced variance of cosmological parameters

Abstract

Modern cosmology relies on the assumption of large-scale isotropy and homogeneity of the Universe. However, locally the Universe is inhomogeneous and anisotropic. So, how can local measurements (at the 100 Mpc scale) be used to determine global cosmological parameters (defined at the 10 Gpc scale)? We use Buchert's averaging formalism and determine a set of locally averaged cosmological parameters in the context of the flat Lambda cold dark matter model. We calculate their ensemble means (i.e. their global values) and variances (i.e. their cosmic variances). We apply our results to typical survey geometries and focus on the study of the effects of local fluctuations of the curvature parameter. By this means we show, that in the linear regime cosmological backreaction and averaging can be reformulated as the issue of cosmic variance. The cosmic variance is found largest for the curvature parameter and discuss some of its consequences. We further propose to use the observed variance of cosmological parameters to measure the growth factor. [abbreviated]