Light propagation and the average expansion rate in near-FRW universes

TL;DR

This paper investigates how small metric perturbations in near-FRW universes affect light propagation and the average expansion rate, revealing that some observables remain close to FRW predictions while others do not.

Contribution

It demonstrates that under specific conditions, the average expansion rate and redshift stay close to FRW values despite second spatial derivatives not being constrained.

Findings

Redshift and average expansion rate are close to FRW in near-FRW universes.

Angular diameter distance can significantly deviate from FRW predictions.

Certain conditions on second derivatives are necessary for these results.

Abstract

We consider universes that are close to Friedmann-Robertson-Walker in the sense that metric perturbations, their time derivatives and first spatial derivatives are small, but second spatial derivatives are not constrained. We show that if we in addition assume that the observer four-velocity is close to its background value and close to the four-velocity which defines the hypersurface of averaging, the redshift and the average expansion rate remain close to the FRW case. However, this is not true for the angular diameter distance. The four-velocity assumption implies certain conditions on second derivatives of the metric and/or the matter content.