Cosmological parameters from CMB and other data: A Monte Carlo approach

We present a fast Markov chain Monte Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent cosmic microwave background (CMB) experiments and provide parameter constraints, including ${\sigma }_8,$ from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae type Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass ${(m}_{\nu }\lesssim 0.3\mathrm{eV}),$ equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendixes we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters.