# Stochastic Particle Production in a de Sitter Background

## TL;DR

This paper investigates stochastic particle production in a de Sitter universe, modeling the effects of random mass variations and non-adiabatic events on scalar fields, revealing log-normal distributions and a Wiener process behavior.

## Contribution

It introduces a transfer matrix approach to analyze stochastic particle production, deriving a Fokker-Planck equation for the evolution of system parameters in a de Sitter background.

## Key findings

- Field amplitudes follow a log-normal distribution.
- Logarithm of the field amplitude behaves like a Wiener process.
- Analytical solutions for distributions in the weak-scattering limit.

## Abstract

We explore non-adiabatic particle production in a de Sitter universe for a scalar spectator field, by allowing the effective mass $m^2(t)$ of this field and the cosmic time interval between non-adiabatic events to vary stochastically. Two main scenarios are considered depending on the (non-stochastic) mass $M$ of the spectator field: the conformal case with $M^2=2H^2$, and the case of a massless field. We make use of the transfer matrix formalism to parametrize the evolution of the system in terms of the "occupation number", and two phases associated with the transfer matrix; these are used to construct the evolution of the spectator field. Assuming short-time interactions approximated by Dirac-delta functions, we numerically track the change of these parameters and the field in all regimes: sub- and super-horizon with weak and strong scattering. In all cases a log-normally distributed field amplitude is observed, and the logarithm of the field amplitude approximately satisfies the properties of a Wiener process outside the horizon. We derive a Fokker-Planck equation for the evolution of the transfer matrix parameters, which allows us to calculate analytically non-trivial distributions and moments in the weak-scattering limit.