Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?

TL;DR

This paper challenges Green and Wald's claim that inhomogeneities have negligible backreaction effects in cosmology, providing counterarguments and demonstrating that their proof is flawed and incomplete.

Contribution

The paper refutes Green and Wald's assertion by critically analyzing their arguments, showing that their proof does not hold in general and that backreaction effects remain relevant.

Findings

Green and Wald's example differs from the actual problem

Their proof of the trace-free property is unphysical

The scheme they use does not account for non-local effects

Abstract

No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that this latter claim is not valid. Specifically, we demonstrate, referring to their recent review paper, that (i) their two-dimensional example used to illustrate the fitting problem differs from the actual problem in important respects, and it assumes what is to be proven; (ii) the proof of the trace-free property of backreaction is unphysical and the theorem about it fails to be a mathematically general statement; (iii) the scheme that underlies the trace-free theorem does not involve averaging and therefore does not capture crucial non-local effects; (iv) their arguments are to a large extent coordinate-dependent, and (v) many of their criticisms of backreaction frameworks do not apply to the published definitions of these frameworks. It is therefore incorrect to infer that Green and Wald have proven a general result that addresses the essential physical questions of backreaction in cosmology.