Sample variance in the local measurements of the Hubble constant

The current $>3\sigma$ tension of the Hubble constant $H_0$ is one of the most highly debated issues in cosmology. While local distance ladder indicates $H_0^{\rm loc}\approx$ 73 $\rm km\ s^{-1}Mpc^{-1}$, cosmic microwave background points to $H_0^{\rm CMB}\approx$ 67 $\rm km\ s^{-1}Mpc^{-1}$. We explore to which extent this tension can be alleviated by the sample variance in the local measurements. Using large-volume cosmological simulations and taking into account the inhomogeneous selection of type Ia supernovae, we find $\sigma(H_0^{\rm loc})$ = 0.31 $\rm km\ s^{-1}Mpc^{-1}$, which is too small to account for the current tension of 6 $\rm km\ s^{-1}Mpc^{-1}$. To explain the current tension would require an underdense region of 150 Mpc with $\delta\approx-0.8$, which is highly unlikely in a $\Lambda$CDM universe and also violates existing observational constraints.