Limits on the Detectability of Cosmic Topology in Hyperbolic Universes

Abstract

We reexamine the possibility of the detection of the cosmic topology in nearly flat hyperbolic Friedmann-Lemaitre-Robertson-Walker (FLRW) universes by using patterns repetition. We update and extend our recent results in two important ways: by employing recent observational constraints on the cosmological density parameters as well as the recent mathematical results concerning small hyperbolic 3-manifolds. This produces new bounds with consequences for the detectability of the cosmic topology. In addition to obtaining new bounds, we also give a concrete example of the sensitive dependence of detectability of cosmic topology on the uncertainties in the observational values of the density parameters.

10 pages, 2 figures, LaTeX2e. To appear in Int. J. Mod. Phys. A (2002). Contribution to the Fifth Alexander Friedmann International Seminar on Gravitation and Cosmology