Critical Dynamics in the Early Universe

TL;DR

This paper explores the critical dynamics of phase transitions during the early universe's inflationary period, introducing a framework that treats slow-roll inflation as a dynamical critical phenomenon influenced by finite size effects in curved spacetime.

Contribution

It develops a novel approach to understanding inflation as a dynamical critical phenomenon using finite size effects and effective actions in curved spacetime.

Findings

Describes symmetry behavior as a finite size effect in curved spacetime

Introduces dynamical finite size effect to explain inflation dynamics

Treats slow-roll inflation as a perturbation of exponential inflation

Abstract

Methods and concepts for the study of phase transitions mediated by a time-dependent order-parameter field in curved spacetimes are discussed. A practical example is the derivation of an effective (quasi-)potential for the description of `slow-roll' inflation in the early universe. We first summarize our early results on viewing the symmetry behavior of constant background fields in curved but static spacetimes as finite size effect, and the use of derivative expansions for constructing effective actions for slowly-varying background fields. We then introduce the notion of dynamical finite size effect to explain how an exponential expansion of the scale factor imparts a finite size to the system and how the symmetry behavior in de Sitter space can be understood qualitatively in this light. We reason why the exponential inflation can be described equivalently by a scale transformation, thus rendering this special class of dynamics as effectively static. Finally we show how, in this view, one can treat the class of `slow-roll' inflation as a dynamic perturbation off the effectively static class of exponential inflation and understand it as a dynamical critical phenomenon in cosmology.