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We review arguably the simplest solution for the Hubble tension -- thepossibility 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 backgroundand other cosmological probes. In addition, since the local supernova sample issparse and highly inhomogeneous, the error bars in the local Hubble constantmight be larger than previously estimated. These two effects -- local matterdensity and sample inhomogeneity -- constitute the sample variance (or thecosmic variance) of the local Hubble constant measurements. To investigatethese effects explicitly, we have mocked up SNIa observations by exactlymatching their actual spatial distribution in a large N-body simulation. Wehave then investigated whether the sample variance is large enough to explainthe Hubble tension. The answer is resoundingly negative: the typical localvariation in $H_0$ is far smaller than what would be required to explain theHubble tension; the latter would require a 20-$\sigma$ deviation from theexpected sample variance. Equivalently, the void required to explain the Hubbletension 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 structurein a $\Lambda$CDM universe. Therefore, the possibility that we live in a voiddoes not come close to explaining the Hubble tension.

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