2005/03/01 by Jesper Gundermann, Gundermann, Jesper · 4 citations
Physics and Astronomy · #Astrophysics (astro-ph) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Noncommutative and Quantum Gravity Theories #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0503014
arxiv created 2005/03/01 · openalex publication_date 2005/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The COBE and the first-year WMAP data both find the CMB quadrupole and octopole to be anomalously low. Here it is shown, that a finite, multi-connected universe may explain this anomaly, supporting earlier analyses [5][18]. A novel technique, pioneered by [16] is used to compute the spectrum and its variance up to k=102. Based on the properties of the Lie group of rotations of S3 it is shown that the spectrum and its variance may be computed solely from the matrix elements of the group-averaging operator, for each of the manifolds S3/I^*, S3/O^* and S3/T^*. Further, it is proved that the spectrum of the CMB may be calculated solely from the radial function, due to the symmetry properties of the Lie-algebra, which is rigorously proven. It is shown, that if the topology of the universe is S3/I^* the uncertainty on the estimates for the total energy density of the universe may be reduced by an order of magnitude. Finally, the paper highlights how the unavailability of an explicit probability function for the observations, given the model, is a challenge for Monte-Carlo simulations of the binary polyhedral spaces which has to be addressed in future work.