Back reaction of inhomogeneities on the expansion: The evolution of cosmological parameters - art. no. 043525

Averaging and evolving inhomogeneities are noncommuting operations. This im plies the existence of deviations of an averaged model from the standard Fr iedmann-Lemaitre cosmologies. We quantify these deviations, encoded in a ba ck reaction parameter, in the framework of Newtonian cosmology. We employ t he linear theory of gravitational instability in the Eulerian and Lagrangia n approaches, as well as the spherically and plane-symmetric solutions as s tandards of reference. We propose a model for the evolution of the average characteristics of a spatial domain for generic initial conditions that con tains the spherical top-hat model and the planar collapse model as exact su bcases. A central result is that the back reaction term itself, calculated on sufficiently large domains, is small but, still, its presence can drive the cosmological parameters on the averaging domain far away from their glo bal values of the standard model. We quantify the variations of these param eters in terms of the fluctuations in the initial data as derived from the power spectrum of initial cold dark matter density fluctuations. For exampl e, in a domain with a radius of 100 Mpc today and initially one-sigma fluct uations, the density parameters deviate from their homogeneous values by 15 %; three-sigma fluctuations lead to deviations larger than 100%.