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