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

TL;DR

The paper develops a fully non-linear framework to predict large-scale CMB anisotropies by generalizing the Sachs-Wolfe effect in terms of the inflationary curvature perturbation ζ. It employs ADM formalism to derive a non-local relation between metric potentials and ζ, and uses a generating-functional approach to compute connected n-point functions, expanding in the small RMS amplitude of perturbations. The authors provide non-perturbative results for the bispectrum and trispectrum in the squeezed limit for single-field inflation, and introduce f_NL and g_NL as parameters characterizing quadratic and cubic primordial non-Gaussianity across different scenarios (including potential non-Gaussian ζ seeds with a_NL, b_NL). This work offers precise theoretical predictions for primordial non-Gaussianity on large angular scales, facilitating comparisons with CMB observations and helping to distinguish primordial signals from late-time or secondary effects.

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.