Constraining topology in harmonic space

Details Constraining topology in harmonic space Constraining topology in harmonic space

2005-10-06

arxiv.org/abs/astro-ph/0510164v2

Phys.Rev.D73:023511,2006

Astronomy and Astrophysics

Astrophysics

19 pages, 16 figures. Updated to match PRD version

Scientific paper

10.1103/PhysRevD.73.023511

We consider several ways to test for topology directly in harmonic space by comparing the measured a_lm with the expected correlation matrices. Two tests are of a frequentist nature while we compute the Bayesian evidence as the third test. Using correlation matrices for cubic and slab-space tori, we study how these tests behave as a function of the minimal scale probed and as a function of the size of the universe. We also apply them to different first-year WMAP CMB maps and confirm that the universe is compatible with being infinitely big for the cases considered. We argue that there is an information theoretical limit (given by the Kullback-Leibler divergence) on the size of the topologies that can be detected.

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