Elements of dodecahedral cosmology

Abstract

A general method for the determination of the harmonics of quotients of the 3-sphere is given. They can all be deduced from three objects already known from Klein. We further show explicitly how these harmonics can be organized in irreducible representations of the holonomy group: this allows for the determination of the full correlation matrix of the Cosmic Microwave Background in the spherical harmonics basis.

18 pages, changed title and expanded explanations, to follow the published version. The results are unchanged

References in corpus (5)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
• CMB Anisotropy of the Poincare Dodecahedron
• Laplacian eigenmodes for spherical spaces
• Invariant operator due to F. Klein quantizes H. Poincare's dodecahedral 3-manifold

Cited by in corpus (4)

• A new analysis of Poincaré dodecahedral space model
• CMB radiation in an inhomogeneous spherical space
• How well-proportioned are lens and prism spaces?
• Waves on accelerating dodecahedral universes