Nonlinear Noise in Cosmology

TL;DR

This paper develops and analyzes exact nonlinear, nonlocal Langevin equations in a cosmological context, revealing effects like mass renormalization and memory functions, with implications for inflaton dynamics and fluctuation-dissipation relations.

Contribution

It introduces a general framework for nonlinear, time-dependent Langevin equations in cosmology, including effects like mass renormalization and memory, and applies it to inflaton-radiation interactions.

Findings

Nonlinearities induce mass renormalization effects.

Time-dependent couplings affect the approach to steady state.

Fluctuation-dissipation theorem remains valid despite nonlinearities.

Abstract

This paper derives and analyzes exact, nonlocal Langevin equations appropriate in a cosmological setting to describe the interaction of some collective degree of freedom with a surrounding ``environment.'' Formally, these equations are much more general, involving as they do a more or less arbitrary ``system,'' characterized by some time-dependent potential, which is coupled via a nonlinear, time-dependent interaction to a ``bath'' of oscillators with time-dependent frequencies. The analysis reveals that, even in a Markov limit, which can often be justified, the time dependences and nonlinearities can induce new and potentially significant effects, such as systematic and stochastic mass renormalizations and state-dependent ``memory'' functions, aside from the standard ``friction'' of a heuristic Langevin description. One specific example is discussed in detail, namely the case of an inflaton field, characterized by a Landau-Ginsburg potential, that is coupled quadratically to a bath of scalar ``radiation.'' The principal conclusion derived from this example is that nonlinearities and time-dependent couplings do {\em not} preclude the possibility of deriving a fluctuation-dissipation theorem, and do {\em not} change the form of the late-time steady state solution for the system, but {\em can} significantly shorten the time scale for the approach towards the steady state.