On non-linear CMB temperature anisotropy from gravitational perturbations

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.