Not empty enough: a local void cannot solve the $H_0$ tension

TL;DR

This paper critically examines the void hypothesis as a solution to the Hubble tension, using simulations to show that local density variations cannot account for the discrepancy in Hubble constant measurements.

Contribution

The study provides the first detailed simulation-based analysis demonstrating that local voids are insufficient to resolve the Hubble tension, challenging a popular proposed solution.

Findings

Sample variance in local Hubble measurements is too small to explain the tension.

A void large enough to resolve the tension would be incompatible with large-scale structure.

Void models require an implausibly empty region, inconsistent with ΛCDM predictions.

Abstract

We review arguably the simplest solution for the Hubble tension -- the possibility that we live in a void. In this scenario, the local Hubble constant $H_0$ is higher than the global value, thus potentially explaining why $H_0$ measured locally by the distance ladder including Type Ia supernovae (SNIa) would be larger than the value inferred from the cosmic microwave background and other cosmological probes. In addition, since the local supernova sample is sparse and highly inhomogeneous, the error bars in the local Hubble constant might be larger than previously estimated. These two effects -- local matter density and sample inhomogeneity -- constitute the sample variance (or the cosmic variance) of the local Hubble constant measurements. To investigate these effects explicitly, we have mocked up SNIa observations by exactly matching their actual spatial distribution in a large N-body simulation. We have then investigated whether the sample variance is large enough to explain the Hubble tension. The answer is resoundingly negative: the typical local variation in $H_0$ is far smaller than what would be required to explain the Hubble tension; the latter would require a 20-$\sigma$ deviation from the expected sample variance. Equivalently, the void required to explain the Hubble tension would need to be so empty ($\delta\approx-0.8$ on a scale 120 $h^{-1}{\rm Mpc}$) that it would be incompatible with the large-scale structure in a $\Lambda$CDM universe. Therefore, the possibility that we live in a void does not come close to explaining the Hubble tension.