Numerical simulation of the stochastic formalism including non-Markovianity

TL;DR

This paper numerically studies stochastic dynamics in cosmology, including non-Markovian effects, by solving coupled Langevin and UV mode equations, revealing significant impacts on field evolution and stationary states.

Contribution

It introduces a numerical method to include non-Markovian effects in stochastic cosmological models by solving IR and UV mode equations simultaneously.

Findings

Effective mass treatment prevents MSSM flat direction saturation.

Memory effects cause quantitative differences in stationary states.

Non-Markovian contributions are significant in strong-coupling regimes.

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; $V=\lambda\phi^4$ and $V=\mu\phi\chi + \lambda\phi^4$, and non-Markovian contributions can lead to quantitative differences, even in stationary configurations, when compared with Markovian approximations, particularly in the strong-coupling regime.