Constraints On The Topology Of The Universe From The WMAP First-Year Sky Maps

Details Constraints On The Topology Of The Universe From The WMAP First-Year Sky Maps Constraints On The Topology Of The Universe From The WMAP First-Year Sky Maps

2004-04-20

arxiv.org/abs/astro-ph/0404400v1

Astrophys.J. 645 (2006) 820-825

Astronomy and Astrophysics

Astrophysics

16 pages, 5 figures

Scientific paper

10.1086/432861

We compute the covariance expected between the spherical harmonic coefficients $a_{\ell m}$ of the cosmic microwave temperature anisotropy if the universe had a compact topology. For fundamental cell size smaller than the distance to the decoupling surface, off-diagonal components carry more information than the diagonal components (the power spectrum). We use a maximum likelihood analysis to compare the Wilkinson Microwave Anisotropy Probe first-year data to models with a cubic topology. The data are compatible with finite flat topologies with fundamental domain $L > 1.2$ times the distance to the decoupling surface at 95% confidence. The WMAP data show reduced power at the quadrupole and octopole, but do not show the correlations expected for a compact topology and are indistinguishable from infinite models.

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