Constraining topology in harmonic space
journal contributionposted on 2023-06-07, 23:33 authored by M Kunz, N Aghanim, L Cayon, O Forni, A Riazuelo, J P Uzan
We consider several ways to test for topology directly in harmonic space by comparing the measured a[script-l]m 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 Wilkinson microwave anisotropy probe 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.
- Published version
JournalPhysical Review D
Department affiliated with
- Physics and Astronomy Publications
NotesI discuss several methods for using the CMB anisotropy correlation matrices to measure cosmic topology. The Bayesian method introduced will be used to analyse Planck satellite data. Correlation matrices computed by Riazuelo and Uzan; otherwise I wrote the paper alone (other authors present for historical reasons).
Full text available