On non-linear CMB temperature anisotropy from gravitational perturbations

TL;DR

This paper calculates third-order non-linear CMB temperature anisotropies on large scales, providing explicit expressions and deriving the bispectrum and trispectrum to understand primordial non-Gaussianity contributions.

Contribution

It offers the first explicit third-order expressions for large-scale CMB anisotropies and separates primordial and non-linear mapping contributions to non-Gaussianity.

Findings

Derived the third-order temperature anisotropy expression in the Sachs-Wolfe limit.

Calculated the bispectrum and trispectrum of CMB anisotropies.

Separated primordial and non-linear mapping contributions to non-Gaussianity.

Abstract

Non-linear CMB temperature anisotropies up to the third-order on large scales are calculated. On large scales and in the Sachs-Wolfe limit, we give the explicit expression for the observed temperature anisotropy in terms of the primordial curvature perturbation up to the third-order. We derived the final bispectrum and trispectrum of anisotropies and the corresponding non-linear parameters, in which the contributions to the observed non-Gaussianity from primordial perturbations and from the non-linear mapping from primordial curvature perturbation to the temperature anisotropy are transparently separated.