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Is there proof that backreaction of inhomogeneities is irrelevant in cosmology? (English) Zbl 1329.83208

Summary: 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.

MSC:

83F05 Relativistic cosmology
85A40 Astrophysical cosmology
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
83C40 Gravitational energy and conservation laws; groups of motions
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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