2005/04/29 by R. Aurich, S. Lustig, Sven Lustig +2
Physics and Astronomy · #Anisotropy #Astrophysics #Black Holes and Theoretical Physics #CMB cold spot #Cosmic microwave background #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Geometry #Homogeneous space #Isometry group #Mathematical physics #Physics #Quantum mechanics #Universe #astro-ph
paper · pdf · doi:10.1088/0264-9381/22/17/006
published as Class.Quant.Grav. 22 (2005) 3443-3460 · A version with high resolution sky maps can be obtained at http://www.physik.uni-ulm.de/theo/qc/
arxiv created 2005/04/29 · openalex publication_date 2005/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The first-year WMAP data taken at their face value hint that the Universe might be slightly positively curved and therefore necessarily finite since all spherical (Clifford–Klein) space forms , given by the quotient of by a group Γ of covering transformations, possess this property. We examine the anisotropy of the cosmic microwave background (CMB) for all typical groups Γ corresponding to homogeneous universes. The CMB angular power spectrum and the temperature correlation function are computed for the homogeneous spaces as a function of the total energy density parameter Ω tot in the large range [1.01, 1.20] and are compared with the WMAP data. We find that out of the infinitely many homogeneous spaces only the three corresponding to the binary dihedral group T ⋆ , the binary octahedral group O ⋆ and the binary icosahedral group I ⋆ are in agreement with the WMAP observations. Furthermore, if Ω tot is restricted to the interval [1.00, 1.04], the space described by T ⋆ is excluded since it requires a value of Ω tot which is probably too large, being in the range [1.06, 1.07]. Thus, for this restrictive case there would remain only the two homogeneous spherical spaces and with Ω tot of about 1.038 and 1.018, respectively, as possible topologies for our Universe.