Cosmic variance of the local Hubble flow in large-scale cosmological simulations

The increasing precision in the determination of the Hubble parameter has reached a per cent level at which large-scale cosmic flows induced by inhomogeneities of the matter distribution become non-negligible. Here, we use large-scale cosmological N-body simulations to study statistical properties of the local Hubble parameter as measured by local observers. We show that the distribution of the local Hubble parameter depends not only on the scale of inhomogeneities, but also on how one defines the positions of observers in the cosmic web and what reference frame is used. Observers located in random dark matter haloes measure on average lower expansion rates than those at random positions in space or in the centres of cosmic voids, and this effect is stronger from the halo rest frames compared to the cosmic microwave background (CMB) rest frame. We compare the predictions for the local Hubble parameter with observational constraints based on Type Ia supernova (SNIa) and CMB observations. Due to cosmic variance, for observers located in random haloes we show that the Hubble constant determined from nearby SNIa may differ from that measured from the CMB by +/-0.8 per cent at 1 sigma statistical significance. This scatter is too small to significantly alleviate a recently claimed discrepancy between current measurements assuming a flat Lambda cold dark matter (Lambda CDM) model. However, for observers located in the centres of the largest voids permitted by the standard Lambda CDM model, we find that Hubble constant measurements from SNIa would be biased high by 5 per cent, rendering this tension non-existent in this extreme case.