2009/09/30 by P. Kramer, Peter Kramer · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #astro-ph.CO
paper · pdf · doi:10.1088/0264-9381/27/9/095013
published as Class.Quant.Grav.27:095013,2010 · 37 pages, 6 figures, in rev5 minor corrections on pp. 17, 18, and 19
openalex publication_date 2010/03/25 · arxiv created 2010/06/12 · arxiv updated 2010/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract\nThe Cosmic Microwave Background CMB originates from an early stage in the history of the universe. Observations show low multipole contributions of CMB fluctuations. A possible explanation is given by a non-trivial topology of the universe and has motivated the search for topological selection rules. Harmonic analysis on a topological manifold must provide basis sets for all functions compatible with a given topology and so is needed to model the CMB fluctuations. We analyze the fundamental groups of Platonic tetrahedral, cubic, and octahedral manifolds using deck transformations. From them we construct the appropriate harmonic analysis and boundary conditions. We provide the algebraic means for modelling the multipole expansion of incoming CMB radiation. From the assumption of randomness we derive selection rules, depending on the point symmetry of the manifold.