Amplification of Primordial Perturbations from the Rise or Fall of the Inflaton

TL;DR

This paper proposes a mechanism within single-field inflation models to amplify small-scale primordial perturbations via step-like features in the inflaton potential, potentially leading to primordial black hole formation.

Contribution

It introduces a novel approach to enhance primordial power spectrum on small scales through potential steps, considering both upward and downward features and their effects on perturbation coupling.

Findings

Perturbations can be sufficiently amplified with rapid potential derivative changes.

Weakly coupled perturbations can still achieve significant enhancement.

Potential steps can induce primordial black hole formation through inflaton trapping.

Abstract

The next generation of cosmic microwave background, gravitational wave, and large scale structure, experiments will provide an unprecedented opportunity to probe the primordial power spectrum on small scales. An exciting possibility for what lurks on small scales is a sharp rise in the primordial power spectrum: This can lead to the formation of primordial black holes, providing a dark matter candidate or the black holes observed by the LIGO-Virgo collaboration. In this work we develop a mechanism for the amplification of the small-scale primordial power spectrum, in the context of single-field inflation with a step-like feature in the inflaton potential. Specifically, we consider both the upward and the downward step in the potential. We also discuss the possibility of the strong coupling between perturbations because the rapid changes of the potential derivatives with the time-dependent field value, caused by the step-like feature, could make the coupling stronger. As a result, we find that the perturbations can remain weakly coupled yet sufficiently enhanced if the step realizes the rapid changes of the potential derivatives in some fraction of an e-fold, $\mathcal O(\mathcal P_{\mathcal R}^{1/2}) \lesssim \Delta N < 1$, where $\mathcal P_\mathcal R$ is the power spectrum of the curvature perturbation at that time. We also discuss the PBH formation rate from the inflaton trapping at the local minimum, which can occur in the potential with an upward step.