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 MicrowaveBackground (CMB) anisotropy in flat and open universes. We develop a formalismto calculate the changes on the radiation power spectrum induced by lensing inthe Newtonian and synchronous-comoving gauges. The previously considerednegligible contribution to the CMB radiation power spectrum of the anisotropicterm of the lensing correlation is shown to be appreciable. However,considering the nonlinear evolution of the matter power spectrum produces onlyslight differences on the results based on linear evolution. The generalconclusion for flat as well as open universes is that lensing slightly smoothesthe radiation power spectrum. For a given range of multipoles the effect oflensing increases with Omega but for the same acoustic peak it decreases with$\Omega$. The maximum contribution of lensing to the radiation power spectrumfor $l\leq 2000$ is $\sim$ 5% for $\Omega$ values in the range 0.1-1.Comment: latex file in ApJ style, 17 pages, 3 ps figure