Non-Gaussianity of Large-Scale Cosmic Microwave Background Anisotropies beyond Perturbation Theory

Abstract

We compute the fully non-linear Cosmic Microwave Background (CMB) anisotropies on scales larger than the horizon at last-scattering in terms of only the curvature perturbation, providing a generalization of the linear Sachs-Wolfe effect at any order in perturbation theory. We show how to compute the n-point connected correlation functions of the large-scale CMB anisotropies for generic primordial seeds provided by standard slow-roll inflation as well as the curvaton and other scenarios for the generation of cosmological perturbations. As an application of our formalism, we compute the three- and four-point connected correlation functions whose detection in future CMB experiments might be used to assess the level of primordial non-Gaussianity, giving the theoretical predictions for the parameters of quadratic and cubic non-linearities f_NL and g_NL.

24 pages, LaTeX file; Revised to match the final version accepted for publication on JCAP (some comments added in Sec.II and V)