Primordial Black Hole Formation from the Upward Step Model: Avoiding Overproduction

TL;DR

This paper examines how non-Gaussian effects in an upward step inflationary model influence primordial black hole formation, showing that non-Gaussianity can both suppress and enhance PBH abundance, resolving overproduction issues.

Contribution

It introduces a revised framework for PBH formation accounting for non-Gaussianity and nonlinearities, challenging previous Gaussian-based assumptions.

Findings

PBH abundance varies non-monotonically with parameter h.

Non-Gaussianity affects gravitational wave signals from PBHs.

Positive f_NL does not always increase PBH production.

Abstract

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 $\mathcal{R}$ 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 $\mathcal{R}(r)$ 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 ($h \simeq 5.9$), 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 $f_{\rm NL}$ does not necessarily enhance PBH production, contrary to conventional expectations. Finally, by accounting for non-perturbative 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.