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 (21)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectrum
• A high resolution foreground cleaned CMB map from WMAP
• Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
• Circles in the Sky: Finding Topology with the Microwave Background Radiation
• Constraining the Topology of the Universe
• A Maximum Likelihood Analysis of the Low CMB Multipoles from WMAP
• A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map
• The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
• Cosmic microwave background anisotropies in multi-connected flat spaces
• Extending the WMAP Bound on the Size of the Universe
• Topological Lensing in Spherical Spaces
• CMB Anisotropy of the Poincare Dodecahedron
• Eigenmodes of 3-dimensional spherical spaces and their application to cosmology
• CMB Anisotropy of Spherical Spaces
• 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
• The circles-in-the-sky signature for three spherical universes
• A spatial correlation analysis for a toroidal universe

Cited by in corpus (15)

• Planck 2013 results. XXVI. Background geometry and topology of the Universe
• Planck 2015 results. XVIII. Background geometry & topology
• The Status of Cosmic Topology after Planck Data
• An improved cosmic crystallography method to detect holonomies in flat spaces
• The residual gravity acceleration effect in the Poincare dodecahedral space
• Topology beyond the horizon: how far can it be probed?
• On the suspected timing error in WMAP map-making
• Deep redshift topological lensing: strategies for the T^3 candidate
• The size of the Universe according to the Poincare dodecahedral space hypothesis
• Cosmic Topology : Twenty Years After
• A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
• There was movement that was stationary, for the four-velocity had passed around
• On the possibility for constraining cosmic topology from the celestial distribution of astronomical objects
• A coordinate-independent technique for detecting globally inhomogeneous flat topologies
• Some spaces are more equal than others