Structure Formation, Backreaction and Weak Gravitational Fields

TL;DR

This paper investigates whether inhomogeneities and backreaction effects in cosmology can cause acceleration, finding that such effects are scale-dependent and generally small, supporting the validity of the perturbed FLRW framework during structure formation.

Contribution

It clarifies the impact of averaging inhomogeneities on cosmic acceleration using a relativistic spherical collapse model, emphasizing scale dependence and the validity of perturbed FLRW during structure formation.

Findings

Averaging can induce apparent acceleration with specific domain choices.

For most of collapse, velocities remain small and perturbed FLRW form is valid.

Effects of inhomogeneities are scale-dependent and generally small on large scales.

Abstract

There is an ongoing debate in the literature as to whether the effects of averaging out inhomogeneities (``backreaction'') in Cosmology can be large enough to account for the acceleration of the scale factor in the FLRW models. In particular, some simple models of structure formation studied in the literature seem to indicate that this is indeed possible, and it has also been suggested that the perturbed FLRW framework is no longer a good approximation during structure formation, when the density contrast becomes nonlinear. In this work we attempt to clarify the situation to some extent, using a fully relativistic model of pressureless spherical collapse. We find that whereas averaging during structure formation can lead to acceleration via a selective choice of averaging domains, the acceleration is not present when more generic domains are used for averaging. Further, we show that for most of the duration of the collapse, matter velocities remain small, and the perturbed FLRW form of the metric can be explicitly recovered, in the structure formation phase. We also discuss the fact that the magnitude of the average effects of inhomogeneities depends on the scale of averaging, and while it may not be completely negligible on intermediate scales, it is expected to remain small when averaging on suitably large scales.