Is backreaction in cosmology a relativistic effect? On the need for an extension of Newton's theory to non-Euclidean topologies

TL;DR

This paper investigates whether cosmological backreaction is inherently a relativistic effect by exploring how non-Euclidean topologies can induce backreaction effects even within a Newtonian framework, challenging previous assumptions.

Contribution

It extends the Buchert-Ehlers theorem to include non-Euclidean topologies, showing that backreaction can be non-zero in Newtonian-like theories with such topologies.

Findings

Backreaction can be non-zero in a Newtonian theory on non-Euclidean topologies.

The implication that backreaction is purely relativistic is not necessarily valid.

The constructed theory remains heuristic and needs further justification from GR limits.

Abstract

Cosmological backreaction corresponds to the effect of inhomogeneities of structure on the global expansion of the Universe. The main question surrounding this phenomenon is whether or not it is important enough to lead to measurable effects on the scale factor evolution eventually explaining its acceleration or the Hubble tension. One of the most important result on this subject is the Buchert-Ehlers theorem (Buchert \& Ehlers, 1997) stating that backreaction is exactly zero when calculated using Newton's theory of gravitation, which may not be the case in general relativity. It is generally said that this result implies that backreaction is a purely relativistic effect. We will show that this is not necessarily the case, in the sense that this implication does not apply to a universe which is still well described by Newton's theory on small scales but has a non-Euclidean topology. The theorem should therefore be generalised to account for such a scenario. In a heuristic calculation where we construct a theory which is locally Newtonian but defined on a non-Euclidean topology, we show that backreaction is non-zero, meaning that it might be non-relativistic depending on the topological class of our Universe. However, that construction is not unique and remains to be justified from a non-relativistic limit of general relativity.