Single Field Double Inflation and Primordial Black Holes
  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.
