Cosmic Microwave Background Anisotropies from Second Order Gravitational Perturbations

This paper presents a complete analysis of the effects of second order gravitational perturbations on cosmic microwave background anisotropies, taking explicitly into account scalar, vector and tensor modes. We also consider the second order perturbations of the metric itself obtaining them, for a universe dominated by a collisionless fluid, in the Poisson gauge, by transforming the known results in the synchronous gauge. We discuss the resulting second order anisotropies in the Poisson gauge, and analyze the possible relevance of the different terms. We expect that, in the simplest scenarios for structure formation, the main effect comes from the gravitational lensing by scalar perturbations that is known to give a few percent contribution to the anisotropies at small angular scales.