Sample variance in the local measurements of the Hubble constant

The current >3σ tension between the Hubble constant H0 measured from local distance indicators and from cosmic microwave background is one of the most highly debated issues in cosmology, as it possibly indicates new physics or unknown systematics. In this work, we explore whether this tension can be alleviated by the sample variance in the local measurements, which use a small fraction of the Hubble volume. We use a large-volume cosmological N-body simulation to model the local measurements and to quantify the variance due to local density fluctuations and sample selection. We explicitly take into account the inhomogeneous spatial distribution of type Ia supernovae. Despite the faithful modelling of the observations, our results confirm previous findings that sample variance in the local Hubble constant ($H$ $^{loc}_{0}$) measurements is small; we find σ ($H$ $^{loc}_{0}$)=0.31km s-1Mpc-1 a nearly negligible fraction of the ~6 km s-1Mpc-1 necessary to explain the difference between the local and global H0 measurements. While the H0 tension could in principle be explained by our local neighbourhood being a underdense region of radius ~150 Mpc, the extreme required underdensity of such a void (δ ≃ -0.8) makes it very unlikely in a ΛCDM universe, and it also violates existing observational constraints. Furthermore, sample variance in a ΛCDM universe cannot appreciably alleviate the tension in H0 measurements even after taking into account the inhomogeneous selection of type Ia supernovae.