Numerical simulation of the stochastic formalism including non-Markovianity

Abstract: We numerically investigate stochastic dynamics in cosmology by solving Langevin equations for Infrared (IR) modes with stochastic noises generated by Ultraviolet (UV) modes at the coarse-graining scale. By construction, the stochastic formalism relies on the separation of scales, which requires solving the equations for UV modes on top of the evolving IR modes for all modes at every time step, leading to a non-Markovian system in general. In this paper, working on a de Sitter background, we analyze several representative models by simultaneously solving the Langevin equations for IR modes and the equations for UV modes at each time step. We demonstrate that once the effects of effective masses are treated consistently by our simulation, the flat direction in the minimal supersymmtric model (MSSM) does not saturate but instead evolves as an exactly flat direction. Furthermore, we investigate memory effects in simple two models; $V=λφ^4$ and $V=μφχ+ λφ^4$, and non-Markovian contributions can lead to quantitative differences, even in stationary configurations, when compared with Markovian approximations, particularly in the strong-coupling regime.