The Local Value of $H_0$ in an Inhomogeneous Universe

TL;DR

This study investigates how local inhomogeneities affect low-redshift $H_0$ measurements, finding only a minor increase of about 0.3% in local estimates, thus not explaining the Hubble tension.

Contribution

It provides a detailed comparison between standard Hubble's law and light-ray based methods in estimating $H_0$ considering inhomogeneities, confirming their minimal impact.

Findings

Inhomogeneities cause a ~0.3% increase in local $H_0$ estimates.

Standard approach slightly underestimates $H_0$ compared to light-ray method.

Inhomogeneities are unlikely to resolve the $H_0$ tension.

Abstract

The effects of local inhomogeneities on low redshift $H_0$ determinations are studied by estimating the redshift-distance relation of mock sources in N-body simulations. The results are compared to those obtained using the standard approach based on Hubble's law. The comparison shows a clear tendency for the standard approach to yield lower values of $H_0$ than the approach based on the scheme using light rays. The difference is, however, small. More precisely, it is found that the overall effect of inhomogeneities on the determination of $H_0$ is a small increase in the local estimates of about $0.3\%$ compared to the results obtained with Hubble's law, when based on a typical distribution of supernovae in the redshift range $0.01 < z < 0.1$. The overall conclusion of the study is a verification of the results that have earlier been obtained by using Hubble's law: The effects of inhomogeneities on local $H_0$ estimates are not significant enough to make it plausible that differences in high- and low-redshift estimates of $H_0$ are due to small inhomogeneities within the setting of standard cosmology.