HIGHER-ORDER GRAVITATIONAL PERTURBATIONS OF THE COSMIC MICROWAVE BACKGROUND

We study the behavior of light rays in perturbed Robertson-Walker cosm ologies, calculating the redshift between an observer and the surface of last scattering to second order in the metric perturbation. At firs t order we recover the classic results of Sachs and Wolfe, and at seco nd order we delineate the various new effects which appear; there is n o a priori guarantee that these effects are significantly smaller than those at first order, since there are large length scales in the prob lem which could lead to sizable prefactors. We find that second-order terms of potential observational interest may be interpreted as transv erse and longitudinal lensing by foreground density perturbations, and a correction to the integrated Sachs-Wolfe effect.