Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation

TL;DR

This paper investigates the bispectrum and one-loop corrections in single-field inflation models with a flat potential region, relevant for primordial black hole formation, confirming theoretical consistency and detailing the perturbation interactions.

Contribution

It provides explicit calculations of the bispectrum during ultraslow-roll inflation and confirms the consistency of one-loop corrections with established perturbation theory.

Findings

Bispectrum satisfies Maldacena's theorem.

One-loop corrections are consistent with second-order in-in perturbation theory.

Generated bispectrum primarily by bulk interactions at the end of inflation.

Abstract

Primordial black holes can be formed from the collapse of large-amplitude perturbation on small scales in the early Universe. Such an enhanced spectrum can be realized by introducing a flat region in the potential of single-field inflation, which makes the inflaton go into a temporary ultraslow-roll period. In this paper, we calculate the bispectrum of curvature perturbation in such a scenario. We explicitly confirm that bispectrum satisfies Maldacena's theorem. At the end of the ultraslow-roll period, the bispectrum is generated by bulk interaction and field redefinition. At the end of inflation, bispectrum is generated only by bulk interaction. We also calculate the one-loop correction to the power spectrum from the bispectrum, called the source method. We find it consistent with the calculation of the one-loop correction from the second-order expansion of in-in perturbation theory.