Spectator field dynamics in de Sitter and curvaton initial conditions

Abstract

We investigate the stochastic behaviour of long wavelength modes of light\nspectator scalar fields during inflation. When starting from a classical field\nvalue, the probability distribution for the spectator both spreads out and\nmoves towards an equilibrium distribution. We study the timescales for a mixed\nquadratic and quartic potential. The timescale of equilibration depends on the\nparameters of the model, and can be surprisingly large, even much more than\nthousands of e-folds. These results imply that the initial conditions for\nspectator fields are not automatically erased during inflation. Applying the\nresults to the curvaton model, we calculate the probability distribution of the\ncurvature perturbation and discuss 'typical' Universes.\n