An Almost FLRW Universe as an Averaged Geometry in Macroscopic Gravity

It is well known that space-time 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 noncommutativity 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-Lemaître-Robertson-Walker (FLRW) model. Namely, we find solutions to the field equations of MG taking the averaged universe to be almost-FLRW modeled using a linearly perturbed FLRW metric. We study several solutions with different functional forms of the metric perturbations including plane-wave ansatzes. We find that back-reaction terms are present not only at the background level but also at the perturbed level, reflecting the nonlinear nature of the averaging process. Thus the averaging effect can extend to both the expansion and the growth of structure in the universe.