The curvature perturbation generated by thermal fluctuations during thermal inflation

TL;DR

This paper investigates how thermal fluctuations during thermal inflation generate curvature perturbations, deriving a formula for the power spectrum based on thermodynamics and the $ abla N$-formalism.

Contribution

It provides a novel calculation of curvature perturbations from thermal fluctuations during thermal inflation using classical thermodynamics and the $ abla N$-formalism.

Findings

Derived the power spectrum of curvature perturbations from thermal fluctuations.

Established the relation between temperature perturbations and curvature perturbations.

Presented a formula for the late-time power spectrum in thermal inflation.

Abstract

During thermal inflation, the temperature determines the number of e-folds of expansion of the universe and so thermal fluctuations are magnified into curvature perturbations. We use classical thermodynamics to calculate the subhorizon thermal fluctuations and trace their evolution into superhorizon temperature perturbations. We convert the temperature perturbations into curvature perturbations using the $\delta N$-formalism, or equivalently the junction condition of curvature perturbations at the end of thermal inflation, denoted by subscript c, and show that the late-time power spectrum is $P_\mathcal{R} = \frac{15}{4\pi^4} \frac{H^3_\mathrm{c}}{g_* T^3_\mathrm{c}} \frac{k^3}{k^3_\mathrm{c}}$.