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 cosmic microwave background (CMB) temperature pattern associated with matched pairs of circles seen in the sky in universes with non-trivial topology. The method is computationally faster than all other statistics developed to hunt for these matched circles. 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 preliminary CMB maps derived from WMAP, but the separation of topological effects from e.g. foregrounds is not straightforward.