Abstract

The stochastic Starobinsky-Yokoyama approach is a powerful non-perturbative effective description of long-wavelength dynamics of a scalar field in de Sitter spacetime. It is based on the observation that on superhorizon distances the field behaves classically, with a noise term produced by subhorizon quantum modes. The approach has been mostly used to calculate the one-point probability distribution of the field, but its real power lies in describing the asymptotic long-distance behaviour of correlation functions through a spectral expansion. I demonstrate this by calculating isocurvature constraints for scalar dark matter models and decay rates of metastable vacua. I also show how to extend the stochastic theory beyond the overdamped approximation used by Starobinsky and Yokoyama. The parameters of this effective theory are determined at one-loop order in perturbation theory, and do not suffer from the same infrared problems as a direct perturbative computation of observables. Therefore the stochastic theory provides a powerful and accurate way of computing cosmological observables.