Applicability of the linearly perturbed FRW metric and Newtonian cosmology

TL;DR

This paper challenges the validity of linear approximations in cosmological models, emphasizing differences between Newtonian gravity and general relativity in the context of structure formation and average expansion rate.

Contribution

It clarifies why linear theory arguments are insufficient for understanding the impact of non-linear density perturbations on cosmic expansion.

Findings

Linear approximations are not valid in non-linear regimes.

Differences between Newtonian gravity and GR are crucial in cosmological modeling.

Linear theory underestimates the effects of structure formation on expansion.

Abstract

It has been argued that the effect of cosmological structure formation on the average expansion rate is negligible, because the linear approximation to the metric remains applicable in the regime of non-linear density perturbations. We discuss why the arguments based on the linear theory are not valid. We emphasise the difference between Newtonian gravity and the weak field, small velocity limit of general relativity in the cosmological setting.