Poincaré dodecahedral space parameter estimates
Abstract
Context: Several studies have proposed that the preferred model of the comoving spatial 3hypersurface of the Universe may be a Poincaré dodecahedral space (PDS) rather than a simply connected, infinite, flat space.
Aims: Here, we aim to improve the surface of last scattering (SLS) optimal crosscorrelation method and apply this to observational data and simulations.
Methods: For a given “generalised” PDS orientation, we analytically derive the formulae required to exclude points on the sky that cannot be members of close SLSSLS crosspairs. These enable more efficient pair selection without sacrificing the uniformity of the underlying selection process. For a sufficiently small matched circle size α and a fixed number of randomly placed points selected for a crosscorrelation estimate, the calculation time is decreased and the number of pairs per separation bin is increased. Using this faster method, and including the smallest separation bin when testing correlations, (i) we recalculate Monte Carlo Markov Chains (MCMC) on the fiveyear Wilkinson Microwave Anisotropy Probe (WMAP) data; and (ii) we seek PDS solutions in a small number of Gaussian random fluctuation (GRF) simulations in order to further explore the statistical significance of the PDS hypothesis.
Results: For 5° < α < 60^circ, a calculation speedup of 310 is obtained. (i) The best estimates of the PDS parameters for the fiveyear WMAP data are similar to those for the threeyear 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 α rather than the twist angle φ. The best estimate of α implies that, given a largescale autocorrelation as weak as that observed, the PDSlike crosscorrelation signal in the WMAP data is expected with a probability of less than about 10%. The expected distribution of φ from the GRF simulations is not uniform on [π,π].
Conclusions: Using this faster algorithm, we find that the previous PDS parameter estimates are stable to the update to fiveyear WMAP data. Moreover, for an infinite, flat, cosmic concordance model with Gaussian random fluctuations, the chance of finding both (a) a largescale autocorrelation as weak as observed; and (b) a PDSlike signal similar to what is observed is less than about 0.015% to 1.25%.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 December 2008
 DOI:
 10.1051/00046361:200810685
 arXiv:
 arXiv:0807.4260
 Bibcode:
 2008A&A...492..657R
 Keywords:

 cosmology: cosmological parameters;
 cosmology: observations;
 cosmology: theory;
 Astrophysics
 EPrint:
 18 pages, 19 figures, accepted in Astronomy &