Cosmic microwave background constraints on multi-connected spherical spaces

Abstract

This article describes the Cosmic Microwave Background anisotropies expected in a closed universe with the topology of a lens space L(p,q) and with density parameter Omega_0 close to 1. It provides the first simulated maps for such spaces along with their corresponding power spectra. In spite of our initial expectations that increasing p (and thus decreasing the size of the fundamental domain) should suppress the quadrupole, we found just the opposite: increasing p elevates the relative power of the low multipoles, for reasons that have since become clear. For Omega_0 = 1.02, an informal ``by eye'' examination of the simulated power spectra suggests that $p$ must be less than 15 for consistency with WMAP's data, while geometric considerations imply that matching circles will exist (potentially revealing the multi-connected topology) only if p > 7. These bounds become less stringent for values of Omega_0 closer to 1.