Poincare dodecahedral space parameter estimates

We aim to improve the surface of last scattering (SLS) optimal cross-correlation method in order to refine estimates of the Poincare dodecahedral space (PDS) cosmological parameters. We analytically derive the formulae required to exclude points on the sky that cannot be members of close SLS-SLS cross-pairs. These enable more efficient pair selection without sacrificing uniformity of the underlying selection process. In certain cases this decreases the calculation time and increases the number of pairs per separation bin. (i) We recalculate Monte Carlo Markov Chains (MCMC) on the five-year WMAP data; and (ii) we seek PDS solutions in a small number of Gaussian random fluctuation (GRF) simulations. For 5 < alpha/deg < 60, a calculation speed-up of 3-10 is obtained. (i) The best estimates of the PDS parameters for the five-year WMAP data are similar to those for the three-year data. (ii) Comparison of the optimal solutions found by the MCMC chains in the observational map to those found in the simulated maps yields a slightly stronger rejection of the simply connected model using $alpha$ than using the twist angle $phi$. The best estimate of $alpha$ implies that_given a large scale auto-correlation as weak as that observed,_ the PDS-like cross-correlation signal in the WMAP data is expected with a probability of less than about 10%. The expected distribution of $phi$ from the GRF simulations is approximately Gaussian around zero, it is not uniform on $[-pi,pi]$. We infer that for an infinite, flat, cosmic concordance model with Gaussian random fluctuations, the chance of finding_both_ (a) a large scale auto-correlation as weak as that observed,_and_ (b) a PDS-like signal similar to that observed is less than about 0.015% to 1.25%.

The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps

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 $phi in {pm 36deg}$. 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-reduc