Backreaction of Cosmological Perturbations in Covariant Macroscopic Gravity

TL;DR

This paper develops a covariant framework for analyzing cosmological backreaction effects of inhomogeneities, providing gauge-invariant expressions applicable to linear and nonlinear perturbations, with results indicating negligible backreaction during matter domination.

Contribution

It adapts Zalaletdinov's covariant Macroscopic Gravity to cosmological perturbation theory, offering gauge-invariant backreaction expressions applicable beyond linear order.

Findings

Backreaction remains negligible during matter-dominated era.

Framework is adaptable to nonlinear structure formation models.

Expressions are applicable to N-body simulations.

Abstract

The problem of corrections to Einstein's equations arising from averaging of inhomogeneities ("backreaction") in the cosmological context, has gained considerable attention recently. We present results of analysing cosmological perturbation theory in the framework of Zalaletdinov's fully covariant Macroscopic Gravity. We show that this framework can be adapted to the setting of cosmological perturbations in a manner which is free from gauge related ambiguities. We derive expressions for the backreaction which can be readily applied in \emph{any} situation (not necessarily restricted to the linear perturbations considered here) where the \emph{metric} can be brought to the perturbed FLRW form. In particular these expressions can be employed in toy models studying nonlinear structure formation, and possibly also in N-body simulations. Additionally, we present results of example calculations which show that the backreaction remains negligible well into the matter dominated era.