The full second-order radiation transfer function for large-scale CMB anisotropies

We calculate the full second-order radiation transfer function for cosmic microwave background anisotropies on large angular scales in a flat universe filled with matter and cosmological constant. It includes (i) the second-order generalization of the Sachs–Wolfe effect, and of (ii) both the early and late integrated Sachs–Wolfe effects, and (iii) the contribution of the second-order tensor modes, and is valid for a generic set of initial conditions specifying the level of primordial non-Gaussianity.