Ralf Aurich

Do we Live in a Small Universe

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 compatible with the possibility that we live in a flat 3-torus with volume 5 × 103 Gpc3.

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 , given by the quotient of by a group ? of covering transformations, possess this property. We examine the anisotropy of the cosmic microwave background (CMB) for all typical groups ? 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 ?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 ?tot is restricted to the interval [1.00, 1.04], the space described by T is excluded since it requires a value of ?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 ?tot of about 1.038 and 1.018, respectively, as possible topologies for our Universe.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.

Hyperbolic universes with a horned topology and the cosmic microwave background 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, 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.

A spatial correlation analysis for a toroidal universe

The spatial cross-correlation function ξC recently introduced by Roukema et al (2008 Astron. Astrophys. 486 55 (arXiv:0801.0006 [astro-ph])) is applied to the equilateral toroidal topology of the universe. Several CMB maps based on the WMAP 5yr data are analysed and a small likelihood in favour of a torus cell is revealed. The results are compared to ten ΛCDM simulations which point to a high false positive rate of the spatial-correlation-function method such that a firm conclusion cannot be drawn.

Cosmic microwave background alignment in multi-connected universes

The low multipoles of the cosmic microwave background (CMB) anisotropy possess some strange properties like the alignment of the quadrupole and the octopole, and the extreme planarity or the extreme sphericity of some multipoles, respectively. In this paper the CMB anisotropy of several multi-connected space forms is investigated with respect to the maximal angular momentum dispersion and the Maxwellian multipole vectors in order to settle the question whether such spaces can explain the low multipole anomalies in the CMB. PACS numbers: 98.80.-k, 98.70.Vc, 98.80.EsThe low multipoles of the cosmic microwave background (CMB) anisotropy possess some strange properties such as the alignment of the quadrupole and the octopole, and the extreme planarity or the extreme sphericity of some multipoles. In this paper, the CMB anisotropy of several multi-connected space forms is investigated with respect to the maximal angular momentum dispersion and the Maxwellian multipole vectors in order to settle the question of whether such spaces can explain the low multipole anomalies in the CMB. The following spaces are considered: the Picard topology in hyperbolic space, three spherical spaces (Poincare dodecahedron, binary tetrahedron and binary octahedron) and a hypertorus in flat space. Although these spaces are able to produce the large-scale suppression of the CMB anisotropy, they do not describe the CMB alignment. From the models considered, the Picard universe shows the strongest alignment properties.

The circles-in-the-sky signature for three spherical universes

The mysteriously low cosmic microwave background (CMB) power on the largest scales might point to a Universe which consists of a multi-connected space. In addition to a suppression of large-scale power, a multi-connected space can be revealed by its circles-in-the-sky signature. In this paper, a detailed search for this signature is carried out for those three homogeneous multi-connected spherical space forms that lead to the smallest large-scale power. A simultaneous search for all occurring paired circles is made using filtered CMB sky maps which enhance the ordinary Sachs-Wolfe contribution. A marginal hint is found for the right-handed Poincare dodecahedron at Ω tot ≃ 1.015 and for the right-handed binary tetrahedral space at Ω tot ≃ 1.068. However, due to the complicated noise and foreground structure of the available microwave sky maps, we cannot draw firm conclusions from our findings.

Hot pixel contamination in the CMB correlation function

Recently, it was suggested that the map-making procedure, which is applied to the time-ordered cosmic microwave background data by the WMAP team, might be flawed by hot pixels. This could lead to a bias in the pixels having an angular distance of about 141° from hot pixels due to the differential measuring process of the satellite WMAP. Here, the bias is confirmed, and the temperature two-point correlation function C(ϑ) is reevaluated by excluding the affected pixels. It is shown that the most significant effect occurs in C(ϑ) at the largest angles near ϑ = 180°. Furthermore, the corrected correlation function C(ϑ) is applied to the cubic topology of the Universe, and it is found that such a multi-connected universe matches the temperature correlation better than the ACDM concordance model, provided the cubic length scale is close to L = 4 measured in units of the Hubble length.

A search for cosmic topology in the final WMAP data

A search for matched circle pairs of similar temperature fluctuations in the final WMAP 9yr data is carried out. Such a signature is expected if the space of the Universe is multi-connected. We investigate the relation between the pixel resolution of CMB maps and a Gaussian smoothing in order to lower the probability for missing matched circle pairs. CMB maps having the 3-torus topology are generated with the characteristics of the WMAP satellite in order to determine how large the smoothing should be chosen in CMB maps disturbed by detector noise. The V and W band data are analysed with respect to matched circle pairs and a tentatively signal is found for a circle pair, which lies, however, close to the plane of the Galaxy. It is, however, inconclusive whether this signal is generated by chance, is due to residual foregrounds contained in the V and W band maps, or is due to a genuine topology.

A survey of lens spaces and large scale CMB anisotropy

The cosmic microwave background (CMB) anisotropy possesses the remarkable property that its power is strongly suppressed on large angular scales. This observational fact can naturally be explained by cosmological models with a non-trivial topology. The paper focuses on lens spaces L(p, q) which are realised by a tessellation of the spherical 3-space S 3 by cyclic Deck groups of order p 6 72. The investigated cosmological parameter space covers the interval tot 2 [1.001,1.05]. Several spaces are found which have CMB correlations on angular scales # > 60 ◦ suppressed by a factor of two compared to the simply-connected S 3 space. The analysis is based on the S statistics, and a comparison to the WMAP 7yr data is carried out. Although the ~

Cosmic topology of polyhedral double-action manifolds

A special class of non-trivial topologies of the spherical space is investigated with respect to their cosmic microwave background (CMB) anisotropies. The observed correlations of the anisotropies on the CMB sky possess on large separation angles surprising low amplitudes which might be naturally be explained by models of the Universe having a multiconnected spatial space. We analysed in Aurich and Lustig (2012 Class. Quantum Grav. 29 215005) the CMB properties of prism double-action manifolds that are generated by a binary dihedral group Dp and a cyclic group Zn up to a group order of 180. Here we extend the CMB analysis to polyhedral double-action manifolds which are generated by the three binary polyhedral groups (T, O, I) and a cyclic group Zn up to a group order of 1000. There are 20 such polyhedral double-action manifolds. Some of them turn out to have even lower CMB correlations on large angles than the Poincare dodecahedron.