Non-Gaussian corrections to the probability distribution of the curvature perturbation from inflation

Abstract

We show how to obtain the probability density function for the amplitude of the curvature perturbation, R, produced during an epoch of slow-roll, single-field inflation, working directly from n-point correlation functions of R. These n-point functions are the usual output of quantum field theory calculations, and as a result we bypass approximate statistical arguments based on the central limit theorem. Our method can be extended to deal with arbitrary forms of non-Gaussianity, appearing at any order in the n-point hierarchy. We compute the probability density for the total smoothed perturbation within a Hubble volume, ε, and for the spectrum of ε. When only the two-point function is retained, exact Gaussian statistics are recovered. When the three-point function is taken into account, we compute explicitly the leading slow-roll correction to the Gaussian result.