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Markov chain Monte Carlo analysis of Bianchi VII_h models | M. Bridges
; J.D. McEwen
; A.N. Lasenby
; M.P. Hobson
; | Date: |
12 May 2006 | Abstract: | We have extended the analysis of Jaffe et al. 2005 & Jaffe et al. 2006 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-year and 3-year 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 marginalised parameter constraints and the comparative Bayesian evidence. With 1-year data we find a Bianchi CMB anisotropy template preferred by a factor of roughly unity in log-evidence over a concordance cosmology alone. For 3-year data this increases slightly to a log-evidence difference of 1.9. This confirms that a Bianchi type template emph{is} supported by the data. The low total energy density of this template, however, implies a geometry that is incompatible with cosmologies inferred from recent CMB observations. Jaffe et al. 2005b found that by 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 year WMAP data would prefer at any significance above $2sigma$. Thus we can confirm the conclusion that a physical Bianchi model is not responsible for this signature, which we have treated in our analysis as merely a template. | Source: | arXiv, astro-ph/0605325 | Services: | Forum | Review | PDF | Favorites |
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