Cold dark matter isocurvature perturbation in the curvaton scenario

We discuss the residual isocurvature perturbations, fully correlated with the curvature perturbation, that are automatic in the curvaton scenario if curvaton decay is sufficiently late. We contrast these residual isocurvature perturbations with the generally uncorrelated ``intrinsic'' isocurvature perturbation generated by an additional field such as the axion. We present a general formula for the residual isocurvature perturbations, referring only to the generation of the relevant quantity [cold dark matter (CDM), baryon number or lepton number] in an unperturbed universe. Specific formulas for the residual isocurvature CDM perturbation are given for most of the commonly considered CDM candidates.