Growth of power spectrum due to decrease of sound speed during inflation

TL;DR

This paper investigates how a small sound speed during inflation amplifies the power spectrum of curvature perturbations, leading to potential primordial black hole formation, with a distinct mechanism from ultraslow-roll inflation.

Contribution

It reveals a new amplification mechanism of the power spectrum due to small sound speed, different from ultraslow-roll inflation, and analyzes the effects of higher-order dispersion corrections.

Findings

Power spectrum remains scale-invariant at large scales.

Transient $k^2$ growth occurs before approaching $k^4$ at small scales.

Amplification can produce enough primordial black holes.

Abstract

We study the amplification of the curvature perturbations due to a small sound speed and find that its origin is different completely from that due to the ultraslow-roll inflation. This is because when the sound speed is very small the enhancement of the power spectrum comes from the fact that the curvature perturbations at the scales smaller than the cosmic microwave background (CMB) scale becomes scale-variant, rather than growing that leads to the amplification of the curvature perturbations during the ultraslow-roll inflation. At large scales the power spectrum of the curvature perturbations remains to be scale invariant, which is consistent with the CMB observations, and then it will have a transient $k^2$ growth and finally approach a $k^4$ growth as the scale becomes smaller and smaller. Thus the power spectrum can be enhanced to generate a sizable amount of primordial black holes. Furthermore, when the high order correction in the dispersion relation of the curvature perturbations is considered the growth of the power spectrum of the curvature perturbations has the same origin as that in the case without this correction.