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Primordial black holes (PBHs) can form in the early Universe from the collapse of large density fluctuations. Tight observational limits on their abundance constrain the amplitude of the primordial fluctuations on very small scales which cannot otherwise be constrained, with PBHs only forming from the extremely rare large fluctuations. The number of PBHs formed is therefore sensitive to small changes in the shape of the tail of the fluctuation distribution, which itself depends on the amount of non-Gaussianity present. We study, for the first time, how quadratic and cubic local non-Gaussianity of arbitrary size (parametrized by f₍₋ and g₍₋ respectively) affects the PBH abundance and the resulting constraints on the amplitude of the fluctuations on very small scales. Intriguingly we find that even nonlinearity parameters of order unity have a significant impact on the PBH abundance. The sign of the non-Gaussianity is particularly important, with the constraint on the allowed fluctuation amplitude tightening by an order of magnitude as f₍₋ changes from just -0. 5 to 0. 5. We find that if PBHs are observed in the future, then regardless of the amplitude of the fluctuations, non-negligible negative f₍₋ would be ruled out. Finally we show that g₍₋ can have an even larger effect on the number of PBHs formed than f₍₋.
Byrnes et al. (Thu,) studied this question.