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Harmonic polynomials on the Poincaré dodecahedral three-manifold. (English) Zbl 1112.43009

With Lie-algebraic methods a set of orthogonal harmonic polynomials on the Poincaré dodecahedral three-manifold is obtained. The expansion in these polynomials of temperature fluctuations on the cosmic microwave background tests this manifold as a candidate for cosmic topology.

MSC:

43A99 Abstract harmonic analysis
83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
83F05 Relativistic cosmology
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