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

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.