Can COBE see the shape of the universe?

Abstract

In recent years, the large angle COBE--DMR data have been used to place constraints on the size and shape of certain topologically compact models of the universe. Here we show that this approach does not work for generic compact models. In particular, we show that compact hyperbolic models do not suffer the same loss of large angle power seen in flat or spherical models. This follows from applying a topological theorem to show that generic hyperbolic three manifolds support long wavelength fluctuations, and by taking into account the dominant role played by the integrated Sachs-Wolfe effect in a hyperbolic universe.

16 Pages, 5 Figures. Version published in Phys. Rev. D

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• Circles in the Sky: Finding Topology with the Microwave Background Radiation
• CMB polarization as a direct test of Inflation
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• Constraints on the Topology of the Universe: Extension to General Geometries
• Is The Universe Infinite Or Is It Just Really Big?
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• The topology of the universe: the biggest manifold of them all
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• Are Small Hyperbolic Universes Observationally Detectable?
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• A Topological Signature in Cosmic Topology
• A test of the Poincare dodecahedral space topology hypothesis with the WMAP CMB data
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• COBE and Global Topology: An Example of the Application of the Identified Circles Principle
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• New Cosmological Model and Its Implications on Observational Data Interpretation