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

Abstract

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.

16 pages, 5 figures

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• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission
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Cited by in corpus (16)

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• Planck 2013 results. XXVI. Background geometry and topology of the Universe
• Planck 2015 results. XVIII. Background geometry & topology
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• Constraints on the topology of the Universe derived from the 7-year WMAP data
• Imprints of spherical non-trivial topologies on the CMB
• A test of the Poincare dodecahedral space topology hypothesis with the WMAP CMB data
• The Topology and Size of the Universe from CMB Temperature and Polarization Data
• The Topology and Size of the Universe from the Cosmic Microwave Background
• Promise of Future Searches for Cosmic Topology
• Cosmic microwave anisotropies in an inhomogeneous compact flat universe
• On Axial and Plane--Mirror Inhomogeneities in the WMAP3 Cosmic Microwave Background Maps
• Cosmic Topology : Twenty Years After
• Orbifold Line Topology and the Cosmic Microwave Background
• A spatial-correlation analysis of the cubic 3-torus topology based on the Planck 2013 data
• Searching for Stringy Topologies in the Cosmic Microwave Background