  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.
