Non-random phases in non-trivial topologies

We present a new technique for constraining the topology of the universe. The method exploits the existence of correlations in the phases of the spherical harmonic coefficients of the CMB temperature pattern associated with matched pairs of circles seen in the sky in universes with non-trivial topology. Unlike other statistics developed to hunt for these matched circles, the method is computationally fast. We applied the method to a range of simulations with topologies of various forms and on different scales. A characteristic form of phase correlation is found in the simulations. We also applied the method to CMB maps derived from WMAP, but found no evidence of similar effects in the data.