Effects of thermal inflation on small scale density perturbations

TL;DR

This paper analyzes how thermal inflation modifies small-scale density perturbations, showing a significant suppression of the power spectrum at certain scales, which could be tested by future small-scale cosmological observations.

Contribution

It provides an analytical calculation of the evolution of perturbations through thermal inflation and quantifies the resulting suppression of the power spectrum on small scales.

Findings

Power spectrum suppressed by a factor of ~50 at small scales

Suppression scale depends on thermal inflation parameters

Potential detectability via CMB distortions or 21cm observations

Abstract

In cosmological scenarios with thermal inflation, extra eras of moduli matter domination, thermal inflation and flaton matter domination exist between primordial inflation and the radiation domination of Big Bang nucleosynthesis. During these eras, cosmological perturbations on small scales can enter and re-exit the horizon, modifying the power spectrum on those scales. The largest modified scale, $k_\mathrm{b}$, touches the horizon size when the expansion changes from deflation to inflation at the transition from moduli domination to thermal inflation. We analytically calculate the evolution of perturbations from moduli domination through thermal inflation and evaluate the curvature perturbation on the constant radiation density hypersurface at the end of thermal inflation to determine the late time curvature perturbation. Our resulting transfer function suppresses the power spectrum by a factor $\sim 50$ at $k \gg k_\mathrm{b}$, with $k_\mathrm{b}$ corresponding to anywhere from megaparsec to subparsec scales depending on the parameters of thermal inflation. Thus, thermal inflation might be constrained or detected by small scale observations such as CMB distortions or 21cm hydrogen line observations.