We analyse the anisotropy of the cosmic microwave background (CMB) for the Poincaré dodecahedron which is an example for a multi-connected spherical universe. We compare the temperature correlation function and the angular power spectrum for the Poincaré dodecahedral universe with the first-year WMAP data and find that this multi-connected universe can explain the surprisingly low CMB anisotropy on large scales found by WMAP provided that the total energy density parameter Ω tot is in the range 1.016 . . . 1.020. The ensemble average over the primordial perturbations is assumed to be the scale-invariant Harrison-Zel'dovich spectrum. The circles-in-the-sky signature is studied and it is found that the signal of the six pairs of matched circles could be missed by current analyses of CMB sky maps.PACS numbers: 98.70.Vc, 98.80.Es

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

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We compute the effects of a compact flat universe on the angular correlation function, the angular power spectrum, the circles-in-the-sky signature, and the covariance matrix of the spherical harmonics coefficients of the cosmic microwave background radiation using the full Boltzmann physics. Our analysis shows that the Wilkinson Microwave Anisotropy Probe (WMAP) three-year data are well compatible with the possibility that we live in a flat 3-torus with volume ≃ 5 · 10 3 Gpc 3 .

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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, 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 98.70.Vc, 98.80.Es

We present a theory of quantum chaos of the Hadamard-Gutzwiller model, a quantum mechanical system which describes the motion of a particle on a surface of constant negative curvature. The theory is based on periodic-orbit sum rules that can be rigorously derived from the Selberg trace formula and which provide an exact substitute, appropriate for our strongly chaotic system, for the Bohr-Sommerfeld-Einstein quantization rules. Our recent enumeration of the classical periodic orbits enables us to evaluate the sum rules numerically and to demonstrate thereby that the theory provides also a practical method to study the quantum chaos of spectra.