Light path averages in spacetimes with non-vanishing average spatial curvature

TL;DR

This study investigates whether non-zero average spatial curvature affects light path averages in inhomogeneous spacetimes, finding minimal differences and suggesting that curvature does not significantly alter the relationship between different averaging methods.

Contribution

It provides the first detailed analysis of light path averages in Swiss cheese models with non-vanishing background curvature, challenging assumptions about curvature's impact on averaging.

Findings

Differences in mean and dispersion are small across models.

Background curvature does not significantly affect average quantities.

Results support the robustness of averaging methods regardless of curvature.

Abstract

Effects of inhomogeneities on observations have been vastly studied using both perturbative methods, N-body simulations and Swiss cheese solutions to the Einstein equations. In nearly all cases, such studied setups assume vanishing spatial background curvature. While a spatially flat Friedmann-Lemaitre-Robertson-Walker model is in accordance with observations, a non-vanishing curvature is not ruled out. It is therefore important to note that, as has been pointed out in the literature, 1 dimensional averages might not converge to volume averages in non-Euclidean space. If this is indeed the case, it will affect the interpretation of observations in spacetimes with non-vanishing average spatial curvature. This possibility is therefore studied here by computing the integrated expansion rate and shear, the accumulated density contrast, and fluctuations in the redshift-distance relation in Swiss cheese models with different background curvatures. It is found that differences in mean and dispersion of these quantities in the different models are small and naturally attributable to differences in background expansion rate and density contrasts. Thus, the study does not yield an indication that the relationship between 1 dimensional spatial averages and volume averages depends significantly on background curvature.