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

Abstract

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.

16 pages, 5 figures. v2: Minor corrections in text; results unchanged

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