The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
arXiv:0801.0006 · doi:10.1051/0004-6361:20079339
Abstract
Several studies have proposed that the shape of the Universe may be a Poincare dodecahedral space (PDS) rather than an infinite, simply connected, flat space. Both models assume a close to flat FLRW metric of about 30% matter density. We study two predictions of the PDS model. (i) For the correct model, the spatial two-point cross-correlation function, $\ximc$, of temperature fluctuations in the covering space, where the two points in any pair are on different copies of the surface of last scattering (SLS), should be of a similar order of magnitude to the auto-correlation function, $\xisc$, on a single copy of the SLS. (ii) The optimal orientation and identified circle radius for a "generalised" PDS model of arbitrary twist , found by maximising $\ximc$ relative to $\xisc$ in the WMAP maps, should yield . We optimise the cross-correlation at scales < 4.0 h^-1 Gpc using a Markov chain Monte Carlo (MCMC) method over orientation, circle size and . Both predictions were satisfied: (i) an optimal "generalised" PDS solution was found, with a strong cross-correlation between points which would be distant and only weakly correlated according to the simply connected hypothesis, for two different foreground-reduced versions of the WMAP 3-year all-sky map, both with and without the kp2 Galaxy mask: the face centres are ϕ\in [0,2π]$, is about 6-9%.
arXiv comment20 pages, 22 figures, accepted in Astronomy & Astrophysics, software available at http://adjani.astro.umk.pl/GPLdownload/dodec/ and MCMCs at http://adjani.astro.umk.pl/GPLdownload/MCMC
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