  Primordial Black Holes (PBHs) have entered the forefront of theoretical
cosmology, due their potential role in phenomena ranging from gravitational
waves, to dark matter, to galaxy formation. While producing PBHs from
inflationary fluctuations naively would seem to require a large deceleration of
the inflaton from its velocity at the horizon exit of CMB scales, in this work
we demonstrate that an acceleration from a relatively small downward step in
the potential that is transited in much less than an e-fold amplifies
fluctuations as well. Depending on the location of the step, such PBHs could
explain dark matter or the black holes detected by the gravitational wave
interferometers. The perturbation enhancement has a natural interpretation as
particle production due to the non-adiabatic transition associated with the
step.
