Solving the Inverse Problem with Inhomogeneous Universes

TL;DR

This paper constructs an inhomogeneous LTB universe model that replicates the distance-redshift relation of the standard $\Lambda$CDM model, and explores observational differences such as redshift variation.

Contribution

It introduces a novel inhomogeneous universe model matching $\Lambda$CDM distance relations and analyzes how local clumpiness and inhomogeneities affect observational signatures.

Findings

Inhomogeneous LTB model can mimic $\Lambda$CDM distance-redshift relation.

Local clumpiness reduces the required large-scale inhomogeneity.

Temporal redshift variation can distinguish the models observationally.

Abstract

We construct the Lema\^itre-Tolman-Bondi (LTB) dust universe whose distance-redshift relation is equivalent to that in the concordance $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological model. In our model, the density distribution and velocity field are not homogeneous, whereas the big-bang time is uniform, which implies that the universe is homogeneous at its beginning. We also study the effects of local clumpiness in the density distribution as well as the effects of large-scale inhomogeneities on the distance-redshift relation, and show that these effects may reduce the amplitude of large-scale inhomogeneities necessary for having a distance-redshift relation that is the same as that of the concordance $\Lambda$CDM universe. We also study the temporal variation of the cosmological redshift and show that, by the observation of this quantity, we can distinguish our LTB universe model from the concordance $\Lambda$CDM model, even if their redshift-distance relations are equivalent to each other.