Cosmology Without Averaging

Abstract

We construct cosmological models consisting of large numbers of identical, regularly spaced masses. These models do not rely on any averaging procedures, or on the existence of a global Friedmann-Robertson-Walker (FRW) background. They are solutions of Einstein's equations up to higher order corrections in a perturbative expansion, and have large-scale dynamics that are well modelled by the Friedmann equation. We find that the existence of arbitrarily large density contrasts does not change either the magnitude or scale of the background expansion, at least when masses are regularly arranged, and up to the prescribed level of accuracy. We also find that while the local space-time geometry inside each cell can be described as linearly perturbed FRW, one could argue that a more natural description is that of perturbed Minkowski space (in which case the scalar perturbations are simply Newtonian potentials). We expect these models to be of use for understanding and testing ideas about averaging in cosmology, as well as clarifying the relationship between global cosmological dynamics and the static space-times associated with isolated masses.