The relation of local measures of Hubble's constant to its global value

Observed large-scale structure and peculiar velocity fields suggest that the local expansion rate, i. e. , local value of Hubble's constant, must vary from place to place. To quantify the issue, we examine the distributions of fractional deviations of local values from the global H₀_ that observers with perfect distance data would find if they surveyed specified volumes of the universe. We use new, very large-scale (N = 10⁷. 2^ particles) calculations of two popular scenarios for the origin of structure, "CDM" and "PIB, " the first having OMEGA₀_ = 1 and the second OMEGA₀_ = 0. 2 to simulate such observations. We find that the expected deviations, due to large-scale motions, are larger than quoted observational errors unless very large (H₀R> 3000 km/s) volumes are surveyed. Even perfect sampling and distances of all galaxies within a sphere extending out to the distances of the Virgo and Coma clusters would leave 45% and 3% rms uncertainties, respectively, in the global value of H₀_ in the CDM model. There is also a systematic bias between local measures of H₀_ and its global value due to observers (galaxies) tending to be in overdense, decelerated regions. Even if the local expansion rate is known to be 80 +/- 8 km/s/Mpc out to 30h^-1^ Mpc in the North Galactic Cap, the 95% confidence interval on the true global value of H₀_ is 50-128 km/s/Mpc in a CDM model. If the universe actually contains coherent structures with sizes H₀R > 10000 km/s, as suggested by some observations, the actual effects may well be more extreme than those simulated. We show that the local versus global error in an H₀_ determination can be roughly estimated by, and is typically slightly smaller than, the angular variance seen over the sky (in octants) in the expansion rate. Moreover, a very rough correction from the local to the global H₀_ value can be derived from the over or under density of galaxies within the local volume. We find empirically the approximate relation (δH₀_/H₀_) = -0. 6 X δngalOMEGA⁰. 4^. Unfortunately, this correction shows both a substantial statistical scatter and is systematically uncertain (depending on both bias and OMEGA₀_). The open PIB model shows typically less than half the local H₀_ variations seen in the closed CDM model. Thus, observations of expansion rate variations are potentially useful as probes of cosmic structure formation models.