Cosmology Without Averaging
  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.
