Average expansion rate and light propagation in a cosmological Tardis spacetime

TL;DR

This paper constructs a novel cosmological model with inhomogeneities called Tardis regions, demonstrating significant backreaction effects on the universe's expansion and analyzing light propagation and effective equations of state.

Contribution

It presents the first exact inhomogeneous cosmological solution with significant backreaction effects, introducing Tardis regions that are larger inside than their background.

Findings

Average expansion rate can grow relative to the background due to inhomogeneities.

Tardis regions are larger on the inside than the background domain.

Light propagation and effective equations of state are consistent with the model.

Abstract

We construct the first exact statistically homogeneous and isotropic cosmological solution in which inhomogeneity has a significant effect on the expansion rate. The universe is modelled as a Swiss Cheese, with dust FRW background and inhomogeneous holes. We show that if the holes are described by the quasispherical Szekeres solution, their average expansion rate is close to the background under certain rather general conditions. We specialise to spherically symmetric holes and violate one of these conditions. As a result, the average expansion rate at late times grows relative to the background, i.e. backreaction is significant. The holes fit smoothly into the background, but are larger on the inside than a corresponding background domain: we call them Tardis regions. We study light propagation, find the effective equations of state and consider the relation of the spatially averaged expansion rate to the redshift and the angular diameter distance.