THE EFFECT OF WEAK GRAVITATIONAL LENSING ON THE COSMIC MICROWAVE BACKGROUND ANISOTROPY - FLAT VERSUS OPEN UNIVERSE MODELS

We have studied the effect of gravitational lensing on the cosmic micr owave background (CMB) anisotropy in flat and open universes. We devel op a formalism to calculate the changes on the radiation power spectru m induced by lensing in the Newtonian and synchronous-comoving gauges. The previously considered negligible contribution to the CMB radiatio n power spectrum of the anisotropic term of the lensing correlation is shown to be appreciable. However, considering the nonlinear evolution of the matter power spectrum produces only slight differences on the results based on linear evolution. The general conclusion for hat as w ell as open universes is that lensing slightly smooths the radiation p ower spectrum. For a given range of multipoles the effect of lensing i ncreases with SZ but for the same acoustic peak it decreases with Omeg a. The maximum contribution of lensing to the radiation power spectrum for l less than or equal to 2000 is similar to 5% for Omega values in the range 0.1-1.