  We propose a model of inflation capable of generating a population of light
black holes (about $10^{-16}$ - $10^{-14}$ solar masses) that might account for
a significant fraction of the dark matter in the Universe. The effective
potential of the model features an approximate inflection point arising from
two-loop order logarithmic corrections in well-motivated and perturbative
particle physics examples. This feature decelerates the inflaton before the end
of inflation, enhancing the primordial spectrum of scalar fluctuations and
triggering efficient black hole production with a peaked mass distribution. At
larger field values, inflation occurs thanks to a generic small coupling
between the inflaton and the curvature of spacetime. We compute accurately the
peak mass and abundance of the primordial black holes using the Press-Schechter
and Mukhanov-Sasaki formalisms, showing that the slow-roll approximation fails
to reproduce the correct results by orders of magnitude. We study as well a
qualitatively similar implementation of the idea, where the approximate
inflection point is due to competing terms in a generic polynomial potential.
In both models, requiring a significant part of the dark matter abundance to be
in the form of black holes implies a small blue scalar tilt with a sizable
negative running and a tensor spectrum that may be detected by the
next-generation probes of the cosmic microwave background. We also comment on
previous works on the topic.
