On the question of measuring spatial curvature in an inhomogeneous universe

TL;DR

This paper investigates how inhomogeneities in the universe affect the measurement and interpretation of spatial curvature, emphasizing the non-perturbative behavior of curvature modes and their observational implications.

Contribution

It provides a non-perturbative numerical analysis of curvature modes in inhomogeneous spacetimes and clarifies their relation to observable quantities.

Findings

Curvature modes behave differently in inhomogeneous settings compared to homogeneous models.

Observations become sensitive to inhomogeneity-induced curvature effects beyond certain scales.

Local curvature does not necessarily match the global curvature inferred from observations.

Abstract

The curvature of a spacetime, either in a topological sense, or averaged over super-horizon-sized 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 constant-time surfaces, will reproduce the observational effects of global symmetry. Further, the curvature of a constant-time hypersurface is not an observable quantity, and can only be inferred indirectly. Here, we examine the behavior of curvature modes on hypersurfaces of an inhomogeneous spacetime non-perturbatively in a numerical 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.