Nonlinear field theories during homogeneous spatial dilation

TL;DR

This paper investigates how uniform spatial dilation affects the propagation of correlations in nonlinear field theories, revealing that nonlinear dynamics can behave differently from linear ones under expansion, with implications for cosmology and physics.

Contribution

It demonstrates that nonlinear field theories can have complex correlation propagation behavior during spatial dilation, unlike linear theories, and provides analysis using the nonlinear KPZ equation.

Findings

Correlations in linear theories stop propagating if dilation speed exceeds correlation speed.

In nonlinear theories, correlations may stop propagating even if dilation speed is lower than correlation speed.

Nonlinear dynamics during expansion cannot be characterized a priori, affecting models in cosmology and physics.

Abstract

The effect of a uniform dilation of space on stochastically driven nonlinear field theories is examined. This theoretical question serves as a model problem for examining the properties of nonlinear field theories embedded in expanding Euclidean Friedmann-Lema\^{\i}tre-Robertson-Walker metrics in the context of cosmology, as well as different systems in the disciplines of statistical mechanics and condensed matter physics. Field theories are characterized by the speed at which they propagate correlations within themselves. We show that for linear field theories correlations stop propagating if and only if the speed at which the space dilates is higher than the speed at which correlations propagate. The situation is in general different for nonlinear field theories. In this case correlations might stop propagating even if the velocity at which space dilates is lower than the velocity at which correlations propagate. In particular, these results imply that it is not possible to characterize the dynamics of a nonlinear field theory during homogeneous spatial dilation {\it a priori}. We illustrate our findings with the nonlinear Kardar-Parisi-Zhang equation.