Cold Dark Matter Isocurvature Perturbations: Constraints and Model Selection

We use CMB (WMAP and ACBAR), large scale structure (SDSS luminous red galaxies) and supernova (SNLS) data to constrain the possible contribution of CDM isocurvature modes to the primordial perturbation spectrum. We consider three different admixtures with adiabatic modes in a flat $\Lambda$CDM cosmology with no tensor modes: fixed correlations with a single spectral index; general correlations with a single spectral index; and general correlations with independent spectral indices for each mode. For fixed correlations, we verify the WMAP analysis for fully uncorrelated and anti-correlated modes, while for general correlations with a single index we find a small tightening of the constraint on the fractional contribution of isocurvature modes to the observed power over earlier work. For generally-correlated modes and independent spectral indices our results are quite different to previous work, needing a doubling of prior space for the isocurvature spectral index in order to explore adequately the region of high likelihood. Standard Markov-Chain Monte-Carlo techniques proved to be inadequate for this particular application; instead our results are obtained with nested sampling. We also use the Bayesian evidence, calculated simply in the nested-sampling algorithm, to compare models, finding the pure adiabatic model to be favoured over all our isocurvature models. This favouring is such that the logarithm of the Bayes Factor, $\mathrm{ln} B < -2$ for all models and $\mathrm{ln} B < -5$ in the cases of fully anti-correlated modes with a single spectral index (the curvaton scenario) and generally-correlated modes with a single spectral index.