Poincare dodecahedral space parameter estimates

Abstract

We aim to improve the surface of last scattering (SLS) optimal cross-correlation method in order to refine estimates of the Poincaré 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 $\varphi$. 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 $\varphi$ 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%.

18 pages, 19 figures, accepted in Astronomy & Astrophysics, software available at http://cosmo.torun.pl/GPLdownload/dodec/ and MCMCs at http://cosmo.torun.pl/GPLdownload/MCMC/ ; v2: histograms added, several minor changes, matches accepted version

References in corpus (5)

• The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
• A new analysis of Poincaré dodecahedral space model
• Imprints of spherical non-trivial topologies on the CMB
• A test of the Poincare dodecahedral space topology hypothesis with the WMAP CMB data
• A spatial correlation analysis for a toroidal universe