The isocurvature fraction after WMAP 3–year data

I revisit the question of the adiabaticity of initial conditions for cosmological perturbations in view of the 3–year WMAP data. I focus on the simplest alternative to pure adiabatic conditions, namely a superposition of the adiabatic mode and one of the 3 possible isocurvature modes, with the same spectral index as the adiabatic component. I discuss findings in terms of posterior bounds on the isocurvature fraction and Bayesian model selection. The Bayes factor (models likelihood ratio) and the effective Bayesian complexity are computed for several prior ranges for the isocurvature content. I find that the CDM isocurvature fraction is now constrained to be less than about 10%, while the fraction in either the neutrino entropy or velocity mode is below about 20%. Model comparison strongly disfavours mixed models that allow for isocurvature fractions larger than unity, while current data do not allow to distinguish between a purely adiabatic model and models with a moderate (i.e., below about 10%) isocurvature contribution. The conclusion is that purely adiabatic conditions are strongly favoured from a model selection perspective. This is expected to apply in even stronger terms to more complicated superpositions of isocurvature contributions.