Primordial black holes may owe their origin to the small-scale enhancement of
the comoving curvature perturbation generated during inflation. Their mass
fraction at formation is markedly sensitive to possible non-Gaussianities in
such large, but rare fluctuations. We discuss a path-integral formulation which
provides the exact mass fraction of primordial black holes at formation in the
presence of non-Gaussianity. Through a couple of classes of models, one based
on single-field inflation and the other on spectator fields, we show that
restricting to a Gaussian statistics may lead to severe inaccuracies in the
estimate of the mass fraction as well as on the clustering properties of the
primordial black holes.Comment: 21 pages, 2 figures, v2: matching published versio
