Ultra-slow-roll Inflation with Non-perturbative Non-Gaussianity and Scalar Induced Gravitational Waves

An ultra-slow-roll phase during inflation could potentially produce the right abundance of primordial black holes (PBHs) for them to form all of dark matter (DM). We consider such a scenario, carefully treating the transitions from slow to ultra slow roll inflation and back, using a parametrisation of the inflaton potential that can describe inflation from the time when CMB scales crossed out of the horizon until its end. A $δN$ analysis shows that this model can possess $O(1)$ non-Gaussianity. When computing the primordial black hole abundance, we keep the full non-linear relation between curvature perturbations and the density contrast and consider the non-Gaussianity to all orders. We find that $O(1)$ non-Gaussianity is sufficient to enhance the PBH abundance by orders of magnitude, leading to reduced gravitational wave (GW) signals for fixed PBH abundance. The signal to noise ratio is computed for future gravitational wave observatories. We find that, in spite of the reduced strength, the GW signal is well above the sensitivity of LISA if PBHs form a significant component of DM.