Primordial black hole formation from the upward step model: Avoiding overproduction

We investigate the formation of primordial black holes (PBHs) in an upward step inflationary model, where nonlinearities between curvature perturbations and field fluctuations introduce a cutoff, deviating from the Gaussian case. This necessitates a reevaluation of PBH formation, as [Formula: see text] is not the optimal variable for estimating abundance. Using the extended Press–Schechter formalism, we show that non-Gaussianity modifies both the curvature perturbation profile [Formula: see text] and the integration path in probability space, significantly impacting PBH abundance. Our results reveal that the abundance initially increases with the parameter h, which characterizes the relaxation stage after the step. However, beyond a critical value ([Formula: see text]), it sharply declines before rising again. Furthermore, we demonstrate that non-Gaussianity introduces uncertainties in indirect PBH observations via gravitational waves. Notably, we present an example where a positive [Formula: see text] does not necessarily enhance PBH production, contrary to conventional expectations. Finally, by accounting for nonperturbative effects, we resolve the overproduction of PBHs suggested by pulsar timing array (PTA) data, underscoring the critical importance of incorporating non-Gaussianity in future studies.