Eternal inflation in a dissipative and radiation environment: Heated demise of eternity

TL;DR

This paper investigates how dissipation and thermal radiation influence eternal inflation within warm inflation models, revealing that increased dissipation suppresses the self-reproduction regime, contrasting with initial facilitation at lower dissipation levels.

Contribution

It introduces analytical tools and a Sturm-Liouville approach to analyze eternal inflation in warm inflation scenarios, highlighting the impact of dissipation and temperature on self-reproduction.

Findings

Higher dissipation makes eternal inflation harder to achieve.

Warm inflation initially favors self-reproduction at low dissipation.

Analytical expressions for thresholds and probabilities are provided.

Abstract

Eternal inflation is studied in the context of warm inflation. We focus on different tools to analyze the effects of dissipation and the presence of a thermal radiation bath on the fluctuation-dominated regime, for which the self-reproduction of Hubble regions can take place. The tools we explore are the threshold inflaton field and threshold number of e-folds necessary to establish a self-reproduction regime and the counting of Hubble regions, using generalized conditions for the occurrence of a fluctuation-dominated regime. We obtain the functional dependence of these quantities on the dissipation and temperature. A Sturm-Liouville analysis of the Fokker-Planck equation for the probability of having eternal inflation and an analysis for the probability of having eternal points are performed. We have considered the representative cases of inflation models with monomial potentials of the form of chaotic and hilltop ones. Our results show that warm inflation tends to initially favor the onset of a self-reproduction regime for smaller values of the dissipation. As the dissipation increases, it becomes harder than in cold inflation (i.e., in the absence of dissipation) to achieve a self-reproduction regime for both types of models analyzed. The results are interpreted and explicit analytical expressions are given whenever that is possible.