How Many Universes Do There Need To Be?

Abstract

In the simplest cosmological models consistent with General Relativity, the total volume of the Universe is either finite or infinite, depending on whether or not the spatial curvature is positive. Current data suggest that the curvature is very close to flat, implying that one can place a lower limit on the total volume. In a Universe of finite age, the "particle horizon" defines the patch of the Universe which is observable to us. Based on today's best-fit cosmological parameters it is possible to constrain the number of observable Universe sized patches, N_U. Specifically, using the new WMAP data, we can say that there are at least 21 patches out there the same volume as ours, at 95% confidence. Moreover, even if the precision of our cosmological measurements continues to increase, density perturbations at the particle horizon size limit us to never knowing that there are more than about 10^5 patches out there.