CMB temperature anisotropies from third order gravitational perturbations

TL;DR

This paper computes third-order gravitational perturbation effects on CMB anisotropies, including scalar, vector, and tensor modes, and explores their implications for non-Gaussianity and the trispectrum in a flat universe.

Contribution

It provides the first complete third-order calculation of CMB anisotropies incorporating all perturbation types and initial conditions, advancing theoretical predictions of non-Gaussian features.

Findings

Derived non-perturbative solutions for photon geodesics in large scale limit.

Characterized the evolution of gravitational potentials affecting the ISW effect.

Laid groundwork for analyzing the CMB trispectrum and primordial non-Gaussianity.

Abstract

In this paper we present a complete computation of the Cosmic Microwave Background (CMB) anisotropies up to third order from gravitational perturbations accounting for scalar, vector and tensor perturbations. We then specify our results to the large scale limit, providing the evolution of the gravitational potentials in a flat universe filled with matter and cosmological constant which characterizes the Integrated Sachs-Wolfe effect. As a byproduct in the large scale approximation we are able to give non-perturbative solutions for the photon geodesic equations. Our results are the first step to provide a complete theoretical prediction for cubic non-linearities which are particularly relevant for characterizing the level of non-Gaussianity in the CMB through the detection of the four-point angular connected correlation function (trispectrum). For this purpose we also allow for generic initial conditions due to primordial non-Gaussianity.