Warm inflation with a generalized Langevin equation scenario

TL;DR

This paper explores warm inflation models using Langevin and generalized Langevin equations, demonstrating the stationarity and scale-invariance of the perturbed inflaton field and comparing the power spectra to cold inflation.

Contribution

It introduces a generalized Langevin equation framework for warm inflation and shows the perturbed field's properties, supporting the scenario's physical plausibility.

Findings

Perturbed inflaton field exhibits stationarity on large scales.

Power spectrum in generalized Langevin warm inflation resembles cold inflation.

Appropriate fluctuation-dissipation relation can replicate cold inflation spectrum.

Abstract

In this paper, we discuss the warm inflation model with both a Langevin equation and a generalized Langevin equation scenario. As a brief picture to illustrate the basic properties of stochastic differential equation in warm inflation, this paper is started from a simple condition with constant dissipative coefficient. In this model, we prove the perturbed inflaton field exhibits a stationary process on large scale, so the perturbed field has a scale-invariant power spectrum. Then we study the warm inflation with a generalized Langevin equation scenario. The perturbed field in such model also shows a stationary process and the power spectrum is quite similar to the one in cold inflation. If choosing an appropriate fluctuation-dissipation relation, we can get a spectrum same as the cold inflation. In a word, we attempt to show the rationality of warm inflationary scenario via statistical physics method.