# Primordial Black Holes and Local Non-Gaussianity in Canonical Inflation

## TL;DR

This paper demonstrates that primordial black holes cannot be produced in sufficient abundance to account for dark matter in canonical single-field inflation models, even considering local non-Gaussian correlations, unless specific fine-tuned conditions are met.

## Contribution

It provides a detailed analysis showing local non-Gaussianity has minimal effect on PBH formation in slow roll and USR inflation, emphasizing the need for fine-tuning in potential shapes.

## Key findings

- Local non-Gaussianity does not significantly affect PBH abundance in slow roll.
- USR models can have a modest effect on curvature fluctuations, but require rapid transitions.
- Formalisms like in-in and delta N are used to analyze non-Gaussianities.

## Abstract

Primordial black holes (PBHs) cannot be produced abundantly enough to be the dark matter in canonical single-field inflation under slow roll. This conclusion is robust to local non-Gaussian correlations between long- and short-wavelength curvature modes, which we show have no effect in slow roll on local primordial black hole abundances. For the prototypical model which evades this no go, ultra-slow roll (USR), these squeezed non-Gaussian correlations have at most an order unity effect on the variance of PBH-producing curvature fluctuations for models that would otherwise fail to form sufficient PBHs. Moreover, the transition out of USR, which is necessary for a successful model, suppresses even this small enhancement unless it causes a large increase in the inflaton kinetic energy in a fraction of an e-fold, which we call a large and fast transition. Along the way we apply the in-in formalism, the delta N formalism, and gauge transformations to compute non-Gaussianities and illuminate different aspects of the physical origin of these results. Local non-Gaussianity in the squeezed limit does not weaken the Gaussian conclusion that PBHs as dark matter in canonical single-field inflation require a complicated and fine-tuned potential shape with an epoch where slow roll is transiently violated.