Impact of cosmic variance on the local measurement of $H_0$

Abstract

Local measurements of the Hubble expansion rate are affected by structures like galaxy clusters or voids. Here we present a fully relativistic treatment of this effect, studying how clustering modifies the dispersion of the mean distance (modulus)-redshift relation in a standard ΛCDM universe. Our findings is that cosmic variance (i.e. the effects of the local structure) is, for supernova observations at small redshifts (0.01 < z < 0.1), of the same order of magnitude as the current observational errors. The cosmic variance has to be taken into account in local measurements of the Hubble expansion rate and it reduces the tension with the CMB measurement.