Newtonian and Post-Newtonian approximations of the k = 0 Friedmann Robertson Walker Cosmology

TL;DR

This paper compares a newly developed post-Newtonian cosmological approximation with general relativity in flat Friedmann-Robertson-Walker models, showing the new approach accurately reproduces relativistic results unlike the Newtonian theory.

Contribution

It introduces a well-posed post-Newtonian approximation for cosmology and demonstrates its consistency with general relativity in specific cosmological models.

Findings

Post-Newtonian theory matches general relativity results.

Newtonian theory fails to reproduce relativistic outcomes.

New approximation has a well-posed initial value problem.

Abstract

In a previous paper we derived a post-Newtonian approximation to cosmology which, in contrast to former Newtonian and post-Newtonian cosmological theories, has a well-posed initial value problem. In this paper, this new post-Newtonian theory is compared with the fully general relativistic theory, in the context of the k = 0 Friedmann Robertson Walker cosmologies. It is found that the post-Newtonian theory reproduces the results of its general relativistic counterpart, whilst the Newtonian theory does not.