Primordial black hole formation with non-Gaussian curvature perturbations

Abstract

In the context of transient constant-roll inflation near a local maximum, we\nderive the non-perturbative field redefinition that relates a Gaussian random\nfield with the true non-Gaussian curvature perturbation. Our analysis shows the\nemergence of a new critical amplitude $\\zeta_*$, corresponding to perturbations\nthat prevent the inflaton from overshooting the local maximum, thus becoming\ntrapped in the false minimum of the potential. For potentials with a mild\ncurvature at the local maximum (and thus small non-Gaussianity), we recover the\nknown perturbative field redefinition. We apply these results to the formation\nof primordial black holes, and discuss the cases for which $\\zeta_*$ is smaller\nor of the same order than the critical value for collapse of spherically\nsymmetric overdensities. In the latter case, we present a simple potential for\nwhich the power spectrum needs an amplitude 10 times smaller that in the\nGaussian case for producing a sizeable amount of primordial black holes.\n