Cosmic backreaction and Gauss's law

TL;DR

This paper investigates how cosmic backreaction affects the expansion of the universe, highlighting the role of Gauss's law and its implications for alternative gravity theories and cosmological modeling.

Contribution

It demonstrates that Gauss's law is crucial for the validity of the fluid approximation in Newtonian gravity and explores the implications for alternative theories of gravitation.

Findings

Corrections to the homogeneous expansion vanish in an infinite universe.

Gauss's law ensures the equivalence of point mass and fluid descriptions in Newtonian gravity.

Backreaction effects are significant in theories that violate Gauss's law.

Abstract

Cosmic backreaction refers to the general question of whether a homogeneous and isotropic cosmological model is able to predict the correct expansion dynamics of our inhomogeneous Universe. One aspect of this issue concerns the validity of the continuous approximation: does a system of point masses expand the same way as a fluid does? This article shows that it is not exactly the case in Newtonian gravity, although the associated corrections vanish in an infinite Universe. It turns out that Gauss's law is a key ingredient for such corrections to vanish. Backreaction, therefore, generically arises in alternative theories of gravitation, which threatens the trustworthiness of their cosmological tests. This phenomenon is illustrated with a toy model of massive gravity.