Constant roll and primordial black holes
  The constant-roll inflation with small positive value of the constant-roll
parameter $\beta\equiv \frac{\ddot\phi}{H\dot\phi}={\rm const.}$ has been known
to produce a slightly red-tilted curvature power spectrum compatible with the
current observational constraints. In this work, we shed light on the
constant-roll inflation with negative $\beta$ and investigate how a stage of
constant-roll inflation may realize the growth in the primordial curvature
power spectrum necessary to produce a peaked spectrum of primordial black hole
abundance. We first review the behavior of constant-roll models in the range of
parameters $-\frac32<\beta<0$, which allows for a constant-roll attractor stage
generating a blue-tilted curvature power spectrum without superhorizon growth.
As a concrete realization, we consider a potential with two slow-roll stages,
separated by the constant-roll stage, in a way that satisfies the current
constraints on the power spectrum and the primordial black hole abundance. The
model can produce primordial black holes as all dark matter, LIGO-Virgo events,
or OGLE microlensing events. Due to the range of different scalar tilts allowed
by the constant-roll potential, this construction is particularly robust and
testable by future observations.
