Stability analysis for the background equations for inflation with dissipation and in a viscous radiation bath

TL;DR

This paper conducts a comprehensive stability analysis of inflationary background equations considering dissipation and bulk viscosity effects, comparing different thermodynamic theories and applying findings to warm inflation models.

Contribution

It introduces a detailed stability framework for inflation with bulk viscosity, analyzing causal and noncausal thermodynamics and their impact on inflation duration and radiation production.

Findings

Causal theories permit higher bulk viscosities before instability occurs.

Causal theories suppress radiation production due to relaxation effects.

Bulk viscosity coefficients influence the duration of warm inflation.

Abstract

The effects of bulk viscosity are examined for inflationary dynamics in which dissipation and thermalization are present. A complete stability analysis is done for the background inflaton evolution equations, which includes both inflaton dissipation and radiation bulk viscous effects. Three representative approaches of bulk viscous irreversible thermodynamics are analyzed: the Eckart noncausal theory, the linear and causal theory of Israel-Stewart and a more recent nonlinear and causal bulk viscous theory. It is found that the causal theories allow for larger bulk viscosities before encountering an instability in comparison to the noncausal Eckart theory. It is also shown that the causal theories tend to suppress the radiation production due to bulk viscous pressure, because of the presence of relaxation effects implicit in these theories. Bulk viscosity coefficients derived from quantum field theory are applied to warm inflation model building and an analysis is made of the effects to the duration of inflation. The treatment of bulk pressure would also be relevant to the reheating phase after inflation in cold inflation dynamics and during the radiation dominated regime, although very little work in both areas has been done, the methodology developed in this paper could be extended to apply to these other problems.