Stochastic dynamics of multi-waterfall hybrid inflation and formation of primordial black holes

Abstract

We show that a hybrid inflation model with multiple waterfall fields can result in the formation of primordial black holes (PBHs) with an astrophysical size, by using an advanced algorithm to follow the stochastic dynamics of the waterfall fields. This is in contrast to the case with a single waterfall field, where the wavelength of density perturbations is usually too short to form PBHs of the astrophysical scale (or otherwise PBHs are overproduced and the model is ruled out) unless the inflaton potential is tuned. In particular, we demonstrate that PBHs with masses of order 1020 g can form after hybrid inflation consistently with other cosmological observations if the number of waterfall fields is about 5 for the case of instantaneous reheating. Observable gravitational waves are produced from the second-order effect of large curvature perturbations as well as from the dynamics of texture or global defects that form after the waterfall phase transition.