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)

References in corpus (5)

• Non-Gaussianity from Inflation: Theory and Observations
• Gauge-Invariant Temperature Anisotropies and Primordial Non-Gaussianity
• CMB 3-point functions generated by non-linearities at recombination
• Relativistic second-order perturbations of nonzero-Λflat cosmological models and CMB anisotropies
• CMB lensing extraction and primordial non-Gaussianity

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