COSMIC MICROWAVE BACKGROUND ANISOTROPIES FROM 2ND-ORDER GRAVITATIONALPERTURBATIONS

This paper presents a complete analysis of the effects of second order gravitational perturbations on cosmic microwave background anisotropi es, taking explicitly into account scalar, vector and tensor modes. We also consider the second order perturbations of the metric itself obt aining them, for a universe dominated by a collisionless fluid, in the Poisson gauge, by transforming the known results in the synchronous g auge. We discuss the resulting second order anisotropies in the Poisso n gauge, and analyze the possible relevance of the different terms. We expect that, in the simplest scenarios for structure formation, the m ain effect comes from the gravitational lensing by scalar perturbation s that is known to give a few percent contribution to the anisotropies at small angular scales. [S0556-2821(97)02918-4].