Article

# Topology of the Universe from COBE–DMR – a wavelet approach

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(Impact Factor: 5.11). 05/2002; 351(3). DOI: 10.1111/j.1365-2966.2004.07672.x
Source: arXiv

ABSTRACT In this paper we pursue a new technique to search for evidence of a finite Universe, making use of a spherical mexican-hat wavelet decomposition of the microwave background fluctuations. Using the information provided by the wavelet coefficients at several scales we test whether compact orientable flat topologies are consistent with the COBE-DMR data. We consider topological sizes ranging from half to twice the horizon size. A scale-scale correlation test indicates that non-trivial topologies with appropriate topological sizes are as consistent with the COBE-DMR data as an infinite universe. Among the finite models the data seems to prefer a Universe which is about the size of the horizon for all but the hypertorus and the triple-twist torus. For the latter the wavelet technique does not seem a good discriminator of scales for the range of topological sizes considered here, while a hypertorus has a preferred size which is 80% of the horizon. This analysis allows us to find a best fit topological size for each model, although cosmic variance might limit our ability to distinguish some of the topologies. Comment: 10 pages, 13 figures (12 coloured), submitted to MNRAS. Figures 1,2 and 3 are not included but a complete version of the paper with high resolution figures can be downloaded from (http://www.mrao.cam.ac.uk/~graca/topol/)

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Available from: Graca Rocha, Nov 08, 2012
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• "Searches for topology using the CMB began with COBE (Bennett et al. 1996) and found no indications of a nontrivial topology on the scale of the last-scattering surface (e.g., Starobinskij 1993; Sokolov 1993; Stevens et al. 1993; de Oliveira-Costa & Smoot 1995; Levin et al. 1998; Bond et al. 1998, 2000; Rocha et al. 2004; but see also Roukema 2000b,a). With the higher resolution and sensitivity of WMAP, there were indications of low power on large scales which could have had a topological origin (Jarosik et al. 2011; Luminet et al. 2003; Caillerie et al. 2007; Aurich 1999; Aurich et al. 2004, 2005, 2006, 2008; Aurich & Lustig 2013; Lew & Roukema 2008; Roukema et al. 2008; Niarchou et al. 2004), but this possibility was not borne out by detailed real-and harmonic-space analyses in two dimensions (Cornish et al. 2004; Key et al. 2007; Bielewicz & Riazuelo 2009; Dineen et al. 2005; Kunz et al. 2006; Phillips & Kogut 2006; Niarchou & Jaffe 2007). "
##### Article: Planck 2015 results. XVIII. Background geometry & topology
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ABSTRACT: Full-sky CMB maps from the 2015 Planck release allow us to detect departures from global isotropy on the largest scales. We present the first searches using CMB polarization for correlations induced by a non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance $\chi_{rec}$). We specialize to flat spaces with toroidal and slab topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology at a scale below the diameter of the last scattering surface. The limits on the radius $R_i$ of the largest sphere inscribed in the topological domain (at log-likelihood-ratio $\Delta\ln{L}>-5$ relative to a simply-connected flat Planck best-fit model) are $R_i>0.97\chi_{rec}$ for the cubic torus and $R_i>0.56\chi_{rec}$ for the slab. The limit for the cubic torus from the matched-circles search is numerically equivalent, $R_i>0.97\chi_{rec}$ (99% CL) from polarisation data alone. We also perform a Bayesian search for a Bianchi VII$_h$ geometry. In the non-physical setting where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component. However, the cosmological parameters generating this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to Planck data requires an amplitude of $-0.1\pm0.04$ compared to +1 if the model were to be correct. In the physical setting where the Bianchi parameters are fit simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VII$_h$ cosmology and constrain the vorticity of such models to $(\omega/H)_0<7.6\times10^{-10}$ (95% CL). [Abridged]
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• "A detection of dark energy is made at a highly significant level and is used to constrain the dark energy parameters of the cosmological concordance model. In addition to the spherical wavelet applications reviewed in detail here, wavelets on the sphere have also been used to test the global topology of the Universe [40]. This application presents an interesting avenue for further research. "
##### Article: Cosmological Applications of a Wavelet Analysis on the Sphere
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ABSTRACT: The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerful techniques available to cosmologists for placing strong constraints on the cosmological parameters that describe the origin, content and evolution of the Universe. The last decade has witnessed the introduction of wavelet analyses in cosmology and, in particular, their application to the CMB. We review here spherical wavelet analyses of the CMB that test the standard cosmological concordance model. The assumption that the temperature anisotropies of the CMB are a realisation of a statistically isotropic Gaussian random field on the sphere is questioned. Deviations from both statistical isotropy and Gaussianity are detected in the reviewed works, suggesting more exotic cosmological models may be required to explain our Universe. We also review spherical wavelet analyses that independently provide evidence for dark energy, an exotic component of our Universe of which we know very little currently. The effectiveness of accounting correctly for the geometry of the sphere in the wavelet analysis of full-sky CMB data is demonstrated by the highly significant detections of physical processes and effects that are made in these reviewed works.
Journal of Fourier Analysis and Applications 07/2007; 13(4). DOI:10.1007/s00041-006-6918-8 · 1.12 Impact Factor