Primordial black holes as a tool for constraining non-Gaussianity

TL;DR

This paper investigates how quadratic and cubic local non-Gaussianity parameters influence primordial black hole formation, revealing that even small non-Gaussianities significantly affect abundance constraints and future observations could rule out certain non-Gaussian models.

Contribution

It provides the first detailed analysis of the impact of arbitrary size quadratic and cubic non-Gaussianity on primordial black hole abundance constraints.

Findings

Non-Gaussianity parameters of order unity significantly impact PBH abundance.

The sign of f_nl greatly affects the constraints on fluctuation amplitude.

g_nl can influence PBH formation more than f_nl.

Abstract

Primordial Black Holes (PBH's) 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 can not otherwise be constrained, with PBH's only forming from the extremely rare large fluctuations. The number of PBH's 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 (parameterised by f_nl and g_nl respectively) affects the PBH abundance and the resulting constraints on the amplitude of the fluctuations on very small scales. Intriguingly we find that even non-linearity 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_nl changes from just -0.5 to 0.5. We find that if PBH's are observed in the future, then regardless of the amplitude of the fluctuations, non-negligible negative f_nl would be ruled out. Finally we show that g_nl can have an even larger effect on the number of PBH's formed than f_nl.