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 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.

15 pages, 10 figures

References in corpus (11)

• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• A general test of the Copernican Principle
• Constraints on backreaction in dust universes
• A Lockdown Perspective on the Hubble Tension (with comments from the SH0ES team)
• Evaluating backreaction with the peak model of structure formation
• Another look at redshift drift and the backreaction conjecture
• Model independent constraints on the cosmological expansion rate
• Relativistic numerical cosmology with Silent Universes
• General Relativistic Corrections to the Weak Lensing Convergence Power Spectrum
• Emergence of spatial curvature
• Light path averages in spacetimes with non-vanishing average spatial curvature

Cited by in corpus (10)

• Is the Observable Universe Consistent with the Cosmological Principle?
• What is flat ΛCDM, and may we choose it?
• Cosmological distances with general-relativistic ray tracing: framework and comparison to cosmographic predictions
• Cosmology using numerical relativity
• First investigation of void statistics in numerical relativity simulations
• The art of building a smooth cosmic distance ladder in a perturbed universe
• EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes
• Remarks on overestimating the effects of inhomogeneities on the Hubble constant
• Spatial anisotropies from long wavelength scalar and tensor modes
• Backreaction and the Role of Spatial Curvature in the Cosmic Neighborhood