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Detectability of Torus Topology

Published online by Cambridge University Press:  01 July 2015

Ophélia Fabre ,
Simon Prunet  and
Jean-Philippe Uzan
Ophélia Fabre
Affiliation:
Institut d'Astrophysique de Paris, 98 bis boulevard Arago, 75014, Paris, France email: fabre@iap.fr, prunet@iap.fr, uzan@iap.fr Observatoire de Lyon, Université Claude Bernard, Lyon 1, CNRS-UMR 5574, Centre de Recherche Astrophysique de Lyon 9 avenue Charles André, Saint-Genis Laval, F-69230, France
Simon Prunet
Affiliation:
Institut d'Astrophysique de Paris, 98 bis boulevard Arago, 75014, Paris, France email: fabre@iap.fr, prunet@iap.fr, uzan@iap.fr UPMC Université Paris 06, UMR7095, 98 bis Boulevard Arago, F-75014, Paris, France
Jean-Philippe Uzan
Affiliation:
Institut d'Astrophysique de Paris, 98 bis boulevard Arago, 75014, Paris, France email: fabre@iap.fr, prunet@iap.fr, uzan@iap.fr UPMC Université Paris 06, UMR7095, 98 bis Boulevard Arago, F-75014, Paris, France
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Abstract

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The global shape, or topology, of the universe is not constrained by the equations of General Relativity, which only describe the local universe. As a consequence, the boundaries of space are not fixed and topologies different from the trivial infinite Euclidean space are possible. The cosmic microwave background (CMB) is the most efficient tool to study topology and test alternative models. Multi-connected topologies, such as the 3-torus, are of great interest because they are anisotropic and allow us to test a possible violation of isotropy in CMB data. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics encodes a topological signature. This signature can be used to distinguish an infinite space from a multi-connected space on sizes larger than the diameter of the last scattering surface (DLSS). With the help of the Kullback-Leibler divergence, we set the size of the edge of the biggest distinguishable torus with CMB temperature fluctuations and E-modes of polarization to 1.15 DLSS. CMB temperature fluctuations allow us to detect universes bigger than the observable universe, whereas E-modes are efficient to detect universes smaller than the observable universe.

Keywords

cosmic microwave backgroundmethods: statisticaltopologyKullback-Leibler divergencedetectability
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 10 , Symposium S306: Statistical Challenges in 21st Century Cosmology , May 2014 , pp. 139 - 143
Copyright
Copyright © International Astronomical Union 2015 

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