Constant roll and primordial black holes

Abstract: 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.