An Almost-FLRW Universe as the Averaged Geometry in Macroscopic Gravity

TL;DR

This paper investigates how the averaging process in Macroscopic gravity affects an almost-FLRW universe, revealing that back-reaction influences both cosmic expansion and structure growth, with implications for precision cosmology.

Contribution

It applies the MG formalism to perturbed FLRW models, demonstrating the presence of back-reaction effects at both background and perturbation levels.

Findings

Back-reaction terms exist at background and perturbed levels.

Averaging impacts both universe expansion and structure growth.

Non-linear averaging effects are significant in cosmological modeling.

Abstract

It is well-known that spacetime averaging is an operation that does not commute with building the Einstein tensor. In the framework of Macroscopic gravity (MG), a covariant averaging procedure, this non-commutativity gives averaged field equations with an additional correction term known as back-reaction. It is important to explore whether such a term, even if known to be small, may or may not cause any systematic effect for precision cosmology. In this work, we explore the application of the MG formalism to an almost Friedmann-Lema\^itre-Robertson-Walker (FLRW) model. Namely, we find solutions to the field equations of MG taking the averaged universe to be almost-FLRW modelled using a linearly perturbed FLRW metric. We study several solutions with different functional forms of the metric perturbations including plane waves ansatzes. We find that back-reaction terms are present not only at the background level but also at perturbed level, reflecting the non-linear nature of the averaging process. Thus, the averaging effect can extend to both the expansion and the growth of structure in the universe.