On the question of measuring spatial curvature in an inhomogeneous universe
Abstract
The curvature of a spacetime, either in a topological sense, or averaged over superhorizonsized patches, is often equated with the global curvature term that appears in Friedmann's equation. In general, however, the Universe is inhomogeneous, and gravity is a nonlinear theory, thus any curvature perturbations violate the assumptions of the FLRW model; it is not necessarily true that local curvature, averaged over patches of constanttime surfaces, will reproduce the observational effects of global symmetry. Further, the curvature of a constanttime hypersurface is not an observable quantity, and can only be inferred indirectly. Here, we examine the behavior of curvature modes on hypersurfaces of a perturbed spacetime in an exact fully relativistic setting, and how this curvature corresponds with that inferred by observers. We also note the point at which observations become sensitive to the impact of curvature sourced by inhomogeneities on inferred average properties, finding general agreement with past literature.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.07274
 Bibcode:
 2020arXiv201007274T
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, 10 figures