paper

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

arXiv:astro-ph/0604579 · doi:10.1088/1475-7516/2006/07/008

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.

30 pages; uses iopart.cls LaTeX style. v2: Replaced with version accepted by JCAP

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