Bayesian model selection analysis of WMAP3

Abstract

We present a Bayesian model selection analysis of WMAP3 data using our code CosmoNest. We focus on the density perturbation spectral index nS and the tensor-to-scalar ratio r, which define the plane of slow-roll inflationary models. We find that while the Bayesian evidence supports the conclusion that nS 6= 1, the data are not yet powerful enough to do so at a strong or decisive level. If tensors are assumed absent, the current odds are approximately 8 to 1 in favour of nS 6= 1 under our assumptions, when WMAP3 data is used together with external data sets. WMAP3 data on its own is unable to distinguish between the two models. Further, inclusion of r as a parameter weakens the conclusion against the Harrison–Zel’dovich case (nS = 1, r = 0), albeit in a prior-dependent way. In appendices we describe the CosmoNest code in detail, noting its ability to supply posterior samples as well as to accurately compute the Bayesian evidence. We make a first public release of CosmoNest, now available at www.cosmonest.org.