CMB anisotropy of spherical spaces

Abstract

Abstract. 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 M 3 = S 3 /Γ, given by the quotient of S 3 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]. We thus conclude that there remain only the two homogeneous spherical spaces S 3 /O ⋆ and S 3 /I ⋆ with Ω tot of about 1.038 and 1.018, respectively, as possible topologies for our 98.70.Vc, 98.80.Es

Constraints on the global topology and size of the universe from the cosmic microwave background

“…Following these arguments, we will focus our attention entirely on the flat case in this work. Details on the Poincaré dodecahedral space and experimental data analysis are given in (Luminet et al 2003;Roukema 2009;Roukema et al 2004Roukema et al , 2008Caillerie et al 2007; Lew & Roukema 2008;Aurich et al 2005b), and other topologies in (Aurich & Lustig 2010;Niarchou & Jaffe 2007;Aurich et al 2006Aurich et al , 2005aCresswell et al 2006;Aurich et al 2005c;Roukema 2005;Aurich et al 2004;Riazuelo et al 2004;Gomero et al 2002a;Bond et al 2000;Mota et al 2005;Gundermann 2005).…”

A brief introduction to cosmic topology

“…At a first sight this preliminary result seems to rule out topologies whose isometries produce antipodal images of the observer, as for example the Poincaré dodecahedron model [59], or any other homogeneous spherical space with detectable isometries. In this regard, it is important to note the results of the recent articles by Roukema et al [60] and Aurich et al [61], Gundermann [62], and some remarks by Luminet [63], which support the dodecahedron model. Furthermore, since detectable topologies (isometries) do not produce, in general, antipodal correlated circles, a little more can be inferred from the lack of nearly antipodal matched circles.…”

Which FLRW Comoving 3-Manifold Is Preferred Observationally and Theoretically?

“…those with equal sizes in different fundamental directions, are expected to more easily fit the WMAP data than other spaces [9]. Among these, the Poincaré dodecahedral space, S 3 /I * , has become a particularly good (though disputed) candidate given the WMAP CMB data [10,11,12,13,14,15,16,17,18,19,20].…”