We study single-field inflationary models with steep steplike features in the potential that lead to the temporary violation of the slow-roll conditions during the evolution of the inflaton. These features enhance the power spectrum of the curvature perturbations by several orders of magnitude at certain scales and also produce prominent oscillatory patterns. We study analytically and numerically the inflationary dynamics. We describe quantitatively the size of the enhancement, as well as the profile of the oscillations, which are shaped by the number and position of the features in the potential. The induced tensor power spectrum inherits the distinctive oscillatory profile of the curvature spectrum and is potentially detectable by near-future space interferometers. The enhancement of the power spectrum by steplike features, though significant, may be insufficient to trigger the production of a sizable number of primordial black holes if radiation dominates the energy density of the early Universe. However, it can result in sufficient black hole production if the Universe is dominated by nonrelativistic matter. For the latter scenario, we find that deviations from the standard monochromatic profile of the mass spectrum of primordial black holes are possible because of the multiple-peak structure of the curvature power spectrum.

• Received 12 June 2021
• Accepted 19 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.103510