Cosmic Microwave Background Constraints On Lens Spaces

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 a 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 find 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 multiconnected topology) only if p>7. These bounds become less stringent for values of Omega(0) closer to 1.