Nonlinear Structure Formation, Backreaction and Weak Gravitational Fields

TL;DR

This paper demonstrates that in cosmology, the effects of inhomogeneities and nonlinear structure formation on the universe's large-scale metric are negligible, supporting the continued use of the perturbed FLRW framework.

Contribution

The study applies covariant averaging and relativistic modeling to show backreaction effects are small during nonlinear structure formation, validating the perturbed FLRW approximation.

Findings

Backreaction effects are negligibly small during structure formation.

Perturbed FLRW metric remains valid when matter velocities are small.

Numerical calculations confirm minimal backreaction in the toy model.

Abstract

There is an ongoing debate in the literature concerning the effects of averaging out inhomogeneities (``backreaction'') in cosmology. In particular, some simple models of structure formation studied in the literature seem to indicate that the backreaction can play a significant role at late times, and it has also been suggested that the standard perturbed FLRW framework is no longer a good approximation during structure formation, when the density contrast becomes nonlinear. In this work we use Zalaletdinov's covariant averaging scheme (macroscopic gravity or MG) to show that as long as the metric of the Universe can be described by the perturbed FLRW form, the corrections due to averaging remain negligibly small. Further, using a fully relativistic and reasonably generic model of pressureless spherical collapse, we show that as long as matter velocities remain small (which is true in our model), the perturbed FLRW form of the metric can be explicitly recovered. Together, these results imply that the backreaction remains small even during nonlinear structure formation, and we confirm this within the toy model with a numerical calculation.