Expectations for the Difference between Local and Global Measurements of the Hubble Constant

Abstract

There are irreducible differences between the Hubble constant measured locally and the global value. They are due to density perturbations, a finite sample volume (cosmic variance), and a finite number of objects in the sample (sampling variance). We quantify these differences for a suite of COBE-normalized cold dark matter models that are consistent with the observed large-scale structure. For small samples of objects that only extend to 10,000 km s-1, the variance can approach 4%. For the largest samples of Type Ia supernovae (SNe Ia), which include about 40 objects and extend to almost 40,000 km s-1, the variance is 1%-2% and is dominated by sampling variance. Sampling and cosmic variance may be an important consideration in comparing local determinations of the Hubble constant with precision determinations of the global value that will be made from high-resolution maps of cosmic background radiation anisotropy.