The long-short wavelength mode coupling tightens primordial black hole constraints

TL;DR

This paper investigates how mode coupling and non-Gaussianity affect constraints on primordial black hole formation, revealing that non-Gaussian effects can significantly tighten these constraints contrary to previous expectations.

Contribution

It extends previous analyses by including mode coupling effects up to third order, showing that non-Gaussianity can tighten PBH constraints even with negative skew.

Findings

Non-Gaussianity can tighten PBH constraints more than Gaussian assumptions.

Mode coupling effects are significant in PBH formation constraints.

Constraints are highly sensitive to non-Gaussianity parameters and super-horizon perturbations.

Abstract

The effects of non-gaussianity on the constraints on the primordial curvature perturbation power spectrum from primordial black holes (PBHs) are considered. We extend previous analyses to include the effects of coupling between the modes of the horizon scale at the time the PBH forms and super-horizon modes. We consider terms of up to third order in the Gaussian perturbation. For the weakest constraints on the abundance of PBHs in the early universe (corresponding to a fractional energy density of PBHs of $10^{-5}$ at the time of formation), in the case of gaussian perturbations, constraints on the power spectrum are $\mathcal{P}_{\zeta}<0.05$ but can significantly tighter when even a small amount of non-gaussianity is considered, to $\mathcal{P}_{\zeta}<0.01$, and become approximately $\mathcal{P}_{\zeta}<0.003$ in more special cases. Surprisingly, even when there is negative skew (which naively would suggest fewer areas of high density, leading to weaker constraints), we find that the constraints on the power spectrum become tighter than the purely gaussian case - in strong contrast with previous results. We find that the constraints are highly sensitive to both the non-gaussianity parameters as well as the amplitude of super-horizon perturbations.