Post-Newtonian Cosmological Modelling
  We develop a new approach to building cosmological models, in which small
pieces of perturbed Minkowski space are joined together at reflection-symmetric
boundaries in order to form a global, dynamical space-time. Each piece of this
patchwork universe is described using post-Newtonian gravitational physics,
with the large-scale expansion of the universe being an emergent phenomenon.
This approach to cosmology does not require any assumptions about non-local
averaging processes. Our framework clarifies the relation between the
weak-field limit of general relativity, and the cosmological solutions that
result from solving Einstein's equations with a set of symmetry assumptions. It
also allows the effects of structure formation on the large-scale expansion of
the universe to be investigated in an unambiguous way. As an explicit example,
we use this formalism to investigate the cosmological behaviour of a large
number of regularly arranged point-like masses. In this case we find that the
large-scale expansion is well modelled by a Friedmann-like equation that
contains terms that take the form of dust, radiation, and spatial curvature.
The radiation term, while small compared to the dust term, is purely a result
of the non-linearity of Einstein's equations.
