Non-Random Phases in Non-Trivial Topologies

Abstract

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. 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.

5 pages, accepted for publication in MNRAS

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• Testing Gaussian random hypothesis with the cosmic microwave background temperature anisotropies in the three-year WMAP data
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• Statistics of phase correlations as a test for non-Gaussianity of the CMB maps
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• Constraining topology in harmonic space
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• Random-Walk Statistics and the Spherical Harmonic Representation of CMB Maps
• Polarized wavelets and curvelets on the sphere
• Topology beyond the horizon: how far can it be probed?
• Statistical Characterization of Temperature Patterns in Anisotropic Cosmologies
• Cosmological Parameters and Cosmic Topology
• Constraints on the cosmological density parameters and cosmic topology
• Cosmic Microwave Background anisotropies: the power spectrum and beyond