Markov chain Monte Carlo analysis of Bianchi VIIh models

We have extended the previous analyses of Jaffe et al. to a complete Markov chain Monte Carlo (MCMC) parameter space study of the Bianchi-type VIIh models including a dark energy density, using Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwave background (CMB) data from the 1- and 3-yr releases. Since we perform the analysis in a Bayesian framework our entire inference is contained in the multidimensional posterior distribution from which we can extract marginalized parameter constraints and the comparative Bayesian evidence. Treating the left-handed Bianchi CMB anisotropy as a template centred upon the 'coldspot' in the Southern hemisphere, the parameter estimates derived for the total energy density, 'tightness' and vorticity from 3-yr data are found to be: Omega tot = 0.43 +/- 0.04, h = 0.32 (+0.02)(-0.13), omega = 9.7(-1.5)(+1.6) x 10(-10) with orientation gamma = 337 degrees(+17 degrees)(-23 degrees) . This template is preferred by a factor of roughly unity in log-evidence over a concordance cosmology alone. A Bianchi-type template is supported by the data only if its position on the sky is heavily restricted. All other Bianchi VIIh templates including all right-handed models, are disfavoured. The low total energy density of the preferred template, implies a geometry that is incompatible with cosmologies inferred from recent CMB observations. Jaffe et al. found that extending the Bianchi model to include a term in Omega(Lambda) creates a degeneracy in the Omega(m)-Omega(Lambda) plane. We explore this region fully by MCMC and find that the degenerate likelihood contours do not intersect areas of parameter space that 1- or 3- yr WMAP data would prefer at any significance above 2 sigma. Thus we can confirm the conclusion that a physical Bianchi VIIh model is not responsible for this signature, which we have treated in our analysis as merely a template.