Primordial black holes as a tool for constraining non-Gaussianity

Primordial Black Holes (PBH's) can form in the early Universe from thecollapse of large density fluctuations. Tight observational limits on theirabundance constrain the amplitude of the primordial fluctuations on very smallscales which can not otherwise be constrained, with PBH's only forming from theextremely rare large fluctuations. The number of PBH's formed is thereforesensitive to small changes in the shape of the tail of the fluctuationdistribution, which itself depends on the amount of non-Gaussianity present. Westudy, for the first time, how quadratic and cubic local non-Gaussianity ofarbitrary size (parameterised by f_nl and g_nl respectively) affects the PBHabundance and the resulting constraints on the amplitude of the fluctuations onvery small scales. Intriguingly we find that even non-linearity parameters oforder unity have a significant impact on the PBH abundance. The sign of thenon-Gaussianity is particularly important, with the constraint on the allowedfluctuation amplitude tightening by an order of magnitude as f_nl changes fromjust -0.5 to 0.5. We find that if PBH's are observed in the future, thenregardless of the amplitude of the fluctuations, non-negligible negative f_nlwould be ruled out. Finally we show that g_nl can have an even larger effect onthe number of PBH's formed than f_nl.