### Abstract

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 H_{0} that observers with perfect distance data would find if they surveyed specified volumes of the universe. We use new, very large-scale (N = 10^{7.2} particles) calculations of two popular scenarios for the origin of structure, "CDM" and "PIB," the first having Ω_{0} = 1 and the second Ω_{0} = 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 (H_{0}R > 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 H_{0} in the CDM model. There is also a systematic bias between local measures of H_{0} 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 H_{0} is 50-128 km/s/Mpc in a CDM model. If the universe actually contains coherent structures with sizes H_{0}R > 10 000 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 H_{0} 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 H_{0} value can be derived from the over or under density of galaxies within the local volume. We find empirically the approximate relation (ΔH_{0}/H_{0}) = -0.6×Δn_{gal}Ω^{0.4}. Unfortunately, this correction shows both a substantial statistical scatter and is systematically uncertain (depending on both bias and Ω_{0}). The open PIB model shows typically less than half the local H_{0} variations seen in the closed CDM model. Thus, observations of expansion rate variations are potentially useful as probes of cosmic structure formation models.

Original language | English (US) |
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Pages (from-to) | 1427-1437 |

Number of pages | 11 |

Journal | Astronomical Journal |

Volume | 103 |

Issue number | 5 |

DOIs | |

State | Published - May 1992 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astronomical Journal*,

*103*(5), 1427-1437. https://doi.org/10.1086/116156