A counterexample to claimed COBE constraints on compact toroidal universe models

Roukema, Boudewijn F.

doi:10.1088/0264-9381/17/19/301

Cited by 18 publications

(17 citation statements)

References 38 publications

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“…Previous analysis, based on the COBE data, mainly constrained the topology of a 3-torus (see Refs. [12,13,14,15,16,17,18,19,20,21,22] and Refs. [23,24,25] for reviews of different methods for searching for the topology).…”

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confidence: 99%

Cosmic microwave background anisotropies in multiconnected flat spaces

Weeks²,

et al. 2004

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This article investigates the signature of the seventeen multi-connected flat spaces in cosmic microwave background (CMB) maps. For each such space it recalls a fundamental domain and a set of generating matrices, and then goes on to find an orthonormal basis for the set of eigenmodes of the Laplace operator on that space. The basis eigenmodes are expressed as linear combinations of eigenmodes of the simply connected Euclidean space. A preceding work, which provides a general method for implementing multi-connected topologies in standard CMB codes, is then applied to simulate CMB maps and angular power spectra for each space. Unlike in the 3-torus, the results in most multi-connected flat spaces depend on the location of the observer. This effect is discussed in detail. In particular, it is shown that the correlated circles on a CMB map are generically not back-to-back, so that negative search of back-to-back circles in the WMAP data does not exclude a vast majority of flat or nearly flat topologies.

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confidence: 99%

Cosmic microwave background anisotropies in multiconnected flat spaces

Weeks²,

et al. 2004

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“…If one takes the maximum likelihood value instead, the constraint becomes conspicuously less stringent. Moreover, for some slightly deformed toroidal models, we find that the large-angle power can be flat and the constraint also becomes less stringent N ∼ 8 (see also [31]). …”

Section: Discussionmentioning

confidence: 77%

How large is our Universe?

Inoue

Sugiyama

2003

Phys. Rev. D

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We reexamine constraints on the spatial size of closed toroidal models with cold dark matter and the cosmological constant from cosmic microwave background. We carry out Bayesian analyses using the Cosmic Background Explorer (COBE) data properly taking into account the statistically anisotropic correlation, i.e., off-diagonal elements in the covariance. We find that the COBE constraint becomes more stringent in comparison with that using only the angular power spectrum, if the likelihood is marginalized over the orientation of the observer. For some limited choices of orientations, the fit to the COBE data is considerably better than that of the infinite counterpart. The best-fit matter normalization is increased because of large-angle suppression in the power and the global anisotropy of the temperature fluctuations. We also study several deformed closed toroidal models in which the fundamental cell is described by a rectangular box. In contrast to the cubic models, the large-angle power can be enhanced in comparison with the infinite counterparts if the cell is sufficiently squashed in a certain direction. It turns out that constraints on some slightly deformed models are less stringent. We comment on how these results affect our understanding of the global topology of our universe. 98.70.Vc,98.80.Jk

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“…Work was then done to include the Doppler effects in the analysis (Roukema 2000a). Using COBE –DMR data, this method has also been applied to constrain asymmetric flat 3‐spaces (Roukema 2000b). Intriguing as this possibility is, it has its difficulties.…”

Section: Searching For Topology – Other Methodsmentioning

confidence: 99%

“…While for compact flat models the eigenmodes decomposition has been done successfully, its analytical calculation for compact hyperbolic models is actually impossible. Methods to constrain these spaces include brute force numerical calculation of the eigenmodes (Aurich & Marklof 1996;Aurich 1999;Inoue 1999;Cornish & Spergel 2000;Inoue, Tomita & Sugyiama 2000) the method of images construction of CMB maps , 2000b and of course geometric methods. Using the eigenmodes computed numerically a comparison of the C l values with COBE-DMR data alone seems to not rule out any of the compact hyperbolic (CH) models (Aurich 1999 .…”

Section: S E a R C H I N G F O R To P O L O G Y -Ot H E R M E T H O D Smentioning

confidence: 99%

Topology of the Universe fromCOBE-DMR - a wavelet approach

Rocha

Cayón

Bowen

et al. 2004

Monthly Notices of the Royal Astronomical Society

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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 per cent 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.

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A counterexample to claimed COBE constraints on compact toroidal universe models

Cited by 18 publications

References 38 publications

Cosmic microwave background anisotropies in multiconnected flat spaces

Cosmic microwave background anisotropies in multiconnected flat spaces

How large is our Universe?

Topology of the Universe fromCOBE-DMR - a wavelet approach

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