Hyperbolic Universes with a Horned Topology and the CMB Anisotropy

We analyse the anisotropy of the cosmic microwave background (CMB) in hyperbolic universes possessing a non-trivial topology with a fundamental cell having an infinitely long horn. The aim of this paper is twofold. On the one hand, we show that the horned topology does not lead to a flat spot in the CMB sky maps in the direction of the horn as stated in the literature. On the other hand, we demonstrate that a horned topology having a finite volume could explain the suppression of the lower multipoles in the CMB anisotropy as observed by COBE and WMAP

Ellipticity of Structures in CMB Sky Maps

We study the ellipticity of contour lines in the sky maps of the cosmic microwave background (CMB) as well as other measures of elongation. The sensitivity of the elongation on the resolution of the CMB maps which depends on the pixelization and the beam profile of the detector, is investigated. It is shown that the current experimental accuracy does not allow to discriminate between cosmological models which differ in curvature by Delta Omega_tot=0.05. Analytical expressions are given for the case that the statistical properties of the CMB are those of two-dimensional Gaussian random fields

Can one hear the shape of the Universe?

It is shown that the recent observations of NASA's explorer mission "Wilkinson Microwave Anisotropy Probe" (WMAP) hint that our Universe may possess a non-trivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.Comment: 4 page

CMB Anisotropy of Spherical Spaces

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/Gamma, given by the quotient of S^3 by a group Gamma of covering transformations, possess this property. We examine the anisotropy of the cosmic microwave background (CMB) for all typical groups Gamma 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 Omega_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 Omega_tot is restricted to the interval [1.00, 1.04], the space described by T* is excluded since it requires a value of Omega_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 Omega_tot of about 1.038 and 1.018, respectively, as possible topologies for our Universe.Comment: A version with high resolution sky maps can be obtained at http://www.physik.uni-ulm.de/theo/qc