Features in the Inflaton Potential and the Spectrum of Cosmological Perturbations

TL;DR

This paper reviews how specific features in the inflaton potential can cause significant enhancements in small-scale cosmological perturbations, potentially leading to observable primordial black holes and gravitational waves, with implications for inflation models.

Contribution

It provides a detailed analysis of how inflection points, steep steps, and sharp turns in the inflaton potential affect the primordial power spectrum and secondary gravitational waves in inflation models.

Findings

Features induce strong enhancement of the curvature spectrum.

Characteristic oscillatory patterns appear in the spectrum.

Potential observability of secondary GWs generated by these features.

Abstract

Cosmological perturbations, originating in the quantum fluctuations of the fields that drive inflation, are observed to be nearly scale invariant at the largest scales. At smaller scales, however, perturbations are not severely constrained and might be of particular importance if their amplitude is large. They can trigger the creation of primordial black holes (PBHs) or stochastic gravitational waves (GWs). Small-scale perturbations are generated during the later stages of inflation, when possible strong features in the inflaton potential can break scale invariance and leave characteristic imprints on the spectrum. We focus on and review three types of features: inflection points and steep steps in the potential, as well as sharp turns in the inflationary trajectory in field space. We show that such features induce a strong enhancement of the curvature spectrum within a certain wavenumber range. In particular cases, they also generate characteristic oscillatory patterns that are transferred in the spectrum of secondary GWs, which are potentially observable by operating or designed experiments. We demonstrate these effects through the calculation of the primordial power spectrum and the PBH abundance in the context of $\alpha$-attractors and supergravity (SUGRA) models of inflation.