Markov chain Monte Carlo analysis of Bianchi VII h 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 VII h 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: Ω tot = 0.43 ± 0.04,  h = 0.32 +0.02 −0.13 , ω= 9.7 +1.6 −1.5 × 10 −10 with orientation ). 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 VII h 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 Ω Λ creates a degeneracy in the 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 2σ. Thus we can confirm the conclusion that a physical Bianchi VII h model is not responsible for this signature, which we have treated in our analysis as merely a template.