Multiplicative Noise: Applications in Cosmology and Field Theory

TL;DR

This paper explores the role of multiplicative noise in cosmology and field theory, deriving nonlinear Langevin equations, discussing fluctuation-dissipation relations, and highlighting effects like reduced relaxation times and increased defect nucleation rates.

Contribution

It introduces a generalized approach to modeling multiplicative noise in cosmological and field theoretic systems, extending Langevin equations and analyzing their physical implications.

Findings

Multiplicative noise can significantly reduce relaxation times in cosmological models.

In field theories, such noise enhances the nucleation rate of topological defects.

The paper derives exact nonlinear Langevin equations for systems with one degree of freedom.

Abstract

Physical situations involving multiplicative noise arise generically in cosmology and field theory. In this paper, the focus is first on exact nonlinear Langevin equations, appropriate in a cosmologica setting, for a system with one degree of freedom. The Langevin equations are derived using an appropriate time-dependent generalization of a model due to Zwanzig. These models are then extended to field theories and the generation of multiplicative noise in such a context is discussed. Important issues in both the cosmological and field theoretic cases are the fluctuation-dissipation relations and the relaxation time scale. Of some importance in cosmology is the fact that multiplicative noise can substantially reduce the relaxation time. In the field theoretic context such a noise can lead to a significant enhancement in the nucleation rate of topological defects.