The variance of the locally measured Hubble parameter explained with different estimators

We study the expected variance of measurements of the Hubble constant, H-0, as calculated in either linear perturbation theory or using non-linear velocity power spectra derived from N-body simulations. We compare the variance with that obtained by carrying out mock observations in the N-body simulations, and show that the estimator typically used for the local Hubble constant in studies based on perturbation theory is different from the one used in studies based on N-body simulations. The latter gives larger weight to distant sources, which explains why studies based on N-body simulations tend to obtain a smaller variance than that found from studies based on the power spectrum. Although both approaches result in a variance too small to explain the discrepancy between the value of H-0 from CMB measurements and the value measured in the local universe, these considerations are important in light of the percent determination of the Hubble constant in the local universe.