We extend investigations of infrared dynamics in accelerating universes. In the presence of massless and minimally coupled scalar fields, physical quantities may acquire growing time dependences through quantum fluctuations at super-horizon scales. From a semiclassical viewpoint, it was proposed that these infrared effects can be described by a Langevin equation. In de Sitter space, the stochastic approach has been proved to be equivalent to the leading power resummation of the growing time dependences. In this study, we make the resummation derivation of the Langevin equation in a general accelerating universe. The resulting Langevin equation contains a white noise term and the coefficient of each term is modified by the slow-roll parameter. Furthermore we show that the semiclassical description of the scalar fields leads to the same stochastic equation as far as we adopt an appropriate time coordinate.

The above investigations are performed in models whose nonlinear terms are given by potentials. Therefore the stochastic approach should be extended in another direction, i.e. in models with derivative interactions. If time allows, I also talk about this direction of generalization.