# Single Field Double Inflation and Primordial Black Holes

## TL;DR

This paper explores a single field double inflation model within scalar-tensor theories, showing how it can produce primordial black holes by deviating from slow-roll conditions and matching current inflationary observations.

## Contribution

It introduces a concrete model of double inflation with a non-minimal coupling and polynomial potential, capable of generating primordial black holes without slow-roll approximation.

## Key findings

- The model matches current inflationary observational data.
- It predicts a sizeable primordial black hole population.
- The black hole mass function is approximately lognormal.

## Abstract

Within the framework of scalar-tensor theories, we study the conditions that allow single field inflation dynamics on small cosmological scales to significantly differ from that of the large scales probed by the observations of cosmic microwave background. The resulting single field double inflation scenario is characterised by two consequent inflation eras, usually separated by a period where the slow-roll approximation fails. At large field values the dynamics of the inflaton is dominated by the interplay between its non-minimal coupling to gravity and the radiative corrections to the inflaton self-coupling. For small field values the potential is, instead, dominated by a polynomial that results in a hilltop inflation. Without relying on the slow-roll approximation, which is invalidated by the appearance of the intermediate stage, we propose a concrete model that matches the current measurements of inflationary observables and employs the freedom granted by the framework on small cosmological scales to give rise to a sizeable population of primordial black holes generated by large curvature fluctuations. We find that these features generally require a potential with a local minimum. We show that the associated primordial black hole mass function is only approximately lognormal.