  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.
