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

Abstract

We present a fast Markov Chain Monte-Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent CMB experiments and provide parameter constraints, including σ8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae 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 (mν 0.3 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 appendices 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.

Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

“…Following [52], we used a modified version of the CAMB code [10] to compute the CMB temperature and polarisation anisotropies seeded by the slow-roll scalar and tensor primordial power spectra of equation (45). The parameter space has been sampled by using Markov Chain Monte Carlo (MCMC) methods implemented in the COSMOMC code [11] and using the likelihood estimator provided by the WMAP team [2,4,3,1]. The likelihood code settings have been kept to their default values which include the pixel based analysis at large scales, a Gaussian likelihood for the beam, with diagonal covariance matrix, and point source corrections [3,53,6].…”

“…These exact power spectra are computed mode by mode and fed into a modified Cosmic Background Microwave (CMB) code, here a modified CAMB code [10], which allows us to determine the temperature and polarisation multipole moments. Finally, we explore the corresponding parameters space by using MonteCarlo techniques as implemented in the COSMOMC code [11] together with the likelihood code developed by the WMAP team [2]. This allows us to put constraints on the free parameters characterising the models during the inflationary phase but also, in principle, during the reheating phase although, most of the time, the accuracy of the data is not sufficient to obtain relevant limits on the reheating temperature.…”

Constraints on braneworld inflation from CMB anisotropies

“…[20] coupled to the CosmoMc (Cosmological Monte Carlo) code [21]. This code makes use of a Markov-chain Monte Carlo method to derive the likelihood values of model parameters.…”

Punctuated inflation and the low CMB multipoles

“…We have evaluated the likelihood function using the likelihood code that has been made publicly available by the WMAP team [70]. We have obtained the best fit values for the parameters of our model using COSMOMC [71,72], the publicly available, Markov Chain Monte Carlo (MCMC) code for the parameter estimation of a given cosmological model. The MCMC convergence diagnostics are done on multiple parallel chains using the Gelman and Rubin ("variance of chain means"/"mean of chain variances") R statistics for each parameter, demanding that (R−1) < 0.01, a procedure that essentially looks at the fluctuations amongst the different chains and decides when to terminate the run.…”