Post-Newtonian Cosmological Modelling

TL;DR

This paper introduces a novel cosmological modeling approach that constructs the universe from patched-together perturbed Minkowski spaces using post-Newtonian physics, enabling clear analysis of structure formation effects on expansion.

Contribution

It presents a new framework for cosmology that avoids non-local averaging and links weak-field gravity to large-scale dynamics through a patchwork construction.

Findings

Large-scale expansion modeled by Friedmann-like equations

Radiation effects emerge from Einstein's non-linearity

Framework clarifies relation between local gravity and cosmology

Abstract

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.