Title: CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula,
Abstract: We obtain the non-linear generalization of the Sachs-Wolfe + integrated
Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our
formula is valid at all orders in perturbation theory, is also valid in all
gauges and includes scalar, vector and tensor modes. A direct consequence of
our results is that the maps of the logarithmic temperature anisotropies are
much cleaner than the usual CMB maps, because they automatically remove many
secondary anisotropies. This can for instance, facilitate the search for
primordial non-Gaussianity in future works. It also disentangles the non-linear
ISW from other effects. Finally, we provide a method which can iteratively be
used to obtain the lensing solution at the desired order.