How well is our Universe described by an FLRW model?
Abstract
Extremely well! In the ΛCDM model, the spacetime metric, g_{ab}, of our Universe is approximated by an FLRW metric, g_{ab}^{(0)}, to about one part in 10^{4} or better on both large and small scales, except in the immediate vicinity of very strong field objects, such as black holes. However, derivatives of g_{ab} are not close to derivatives of g_{ab}^{(0)}, so there can be significant differences in the behavior of geodesics and huge differences in curvature. Consequently, observable quantities in the actual Universe may differ significantly from the corresponding observables in the FLRW model. Nevertheless, as we shall review here, we have proven general results showing that—within the framework of our approach to treating backreaction—the large matter inhomogeneities that occur on small scales cannot produce significant effects on large scales, so g_{ab}^{(0)} satisfies Einstein's equation with the averaged stressenergy tensor of matter as its source. We discuss the flaws in some other approaches that have suggested that large backreaction effects may occur. As we also will review here, with a suitable ‘dictionary,’ Newtonian cosmologies provide excellent approximations to cosmological solutions to Einstein's equation (with dust and a cosmological constant) on all scales. Our results thereby provide strong justification for the mathematical consistency and validity of the ΛCDM model within the context of general relativistic cosmology.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 December 2014
 DOI:
 10.1088/02649381/31/23/234003
 arXiv:
 arXiv:1407.8084
 Bibcode:
 2014CQGra..31w4003G
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 Invited contribution to a Classical and Quantum Gravity focus issue on "Relativistic Effects in Cosmology", edited by Kazuya Koyama