The isocurvature fraction after WMAP 3-yr data

I revisit the question of the adiabaticity of initial conditions for cosmological perturbations in view of the 3- yrWilkinson Microwave Anisotropy Probe ( WMAP) data. I focus on the simplest alternative to purely adiabatic conditions, namely a superposition of the adiabatic mode and one of the three 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 cold dark matter isocurvature fraction is now constrained to be less than about 10 per cent, while the fraction in either the neutrino entropy or velocity mode is below about 20 per cent. Model comparison strongly disfavours mixed models that allow for isocurvature fractions larger than unity, while current data do not allow one to distinguish between a purely adiabatic model and models with a moderate ( i. e. below about 10 per cent) 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.