%0 Generic %1 roukema2008optimal %A Roukema, Boudewijn F. %A Bulinski, Zbigniew %A Szaniewska, Agnieszka %A Gaudin, Nicolas E. %D 2008 %K dodecahedral generalised optimal phase poincare %R 10.1051/0004-6361:20079339 %T The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps %U http://arxiv.org/abs/0801.0006 %X 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 $\phi$, found by maximising $\ximc$ relative to $\xisc$ in the WMAP maps, should yield $ın \36\deg\$. 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 $\phi$. 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 $(l,b)_i=1,6(184d, 62d), (305d, 44d), (46d, 49d), (117d, 20d), (176d, -4d), (240d, 13d) to within ~2d, and their antipodes; (ii) this solution has twist \phi= (+39 2.5)d, in agreement with the PDS model. The chance of this occurring in the simply connected model, assuming a uniform distribution $\phi 0,2\pi$, is about 6-9%.

@misc{roukema2008optimal, 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 $\phi$, found by maximising $\ximc$ relative to $\xisc$ in the WMAP maps, should yield $\phi \in \{\pm 36\deg\}$. 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 $\phi$. 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 $(l,b)_{i=1,6}\approx (184d, 62d), (305d, 44d), (46d, 49d), (117d, 20d), (176d, -4d), (240d, 13d) to within ~2d, and their antipodes; (ii) this solution has twist \phi= (+39 \pm 2.5)d, in agreement with the PDS model. The chance of this occurring in the simply connected model, assuming a uniform distribution $\phi \in [0,2\pi]$, is about 6-9%.}, added-at = {2013-12-23T11:08:02.000+0100}, author = {Roukema, Boudewijn F. and Bulinski, Zbigniew and Szaniewska, Agnieszka and Gaudin, Nicolas E.}, biburl = {https://www.bibsonomy.org/bibtex/25bb126449da0c84ab6220b39e4a27aa3/aeu_research}, description = {The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps}, doi = {10.1051/0004-6361:20079339}, interhash = {f2e957a9a1f86b7368352c4527d43711}, intrahash = {5bb126449da0c84ab6220b39e4a27aa3}, keywords = {dodecahedral generalised optimal phase poincare}, note = {cite arxiv:0801.0006Comment: 20 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}, timestamp = {2013-12-23T11:08:02.000+0100}, title = {The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps}, url = {http://arxiv.org/abs/0801.0006}, year = 2008 }