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 ${n}_{\mathrm{S}}$ 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 ${n}_{\mathrm{S}}\ensuremath{\ne}1$, 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 favor of ${n}_{\mathrm{S}}\ensuremath{\ne}1$ 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 (${n}_{\mathrm{S}}=1$, $r=0$), 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.