Curvaton distribution from stochastic inflation

The curvaton paradigm can realise a part of or all the observed curvature perturbation. Based on the stochastic formalism of inflation and closed-form exact distributions therein, the distribution of the curvature perturbation is presented in an analytical manner by identifying a test field with a curvaton. The parameter space consisting of the decay rate and the mass of the curvaton is studied to discuss the probability that the curvaton can contribute to the curvature perturbation in a non-negligible way.