Imprints of spherical non-trivial topologies on the CMB

Abstract

The apparent low power in the CMB temperature anisotropy power spectrum derived from WMAP motivated us to consider the possibility of a non-trivial topology. We focus on some simple spherical multi-connected manifolds (Quaternionic, Octahedral, Truncated Cube and Poincare spaces) and discuss their implications for the CMB in terms of the power spectrum, maps and the correlation matrix. We also perform Bayesian model comparison against the fiducial best-fit LCDM based both on the power spectrum and the correlation matrix to assess their statistical significance. We find that the first year power spectrum shows a slight preference for the Truncated Cube space, but the 3-year data show no evidence for any of these spaces.