The Effect of Weak Gravitational Lensing on the Cosmic Microwave Background Anisotropy: Flat versus Open Universes

We have studied the effect of gravitational lensing on the Cosmic Microwave Background (CMB) anisotropy in flat and open universes. We develop a formalism to calculate the changes on the radiation power spectrum induced by lensing in the Newtonian and synchronous-comoving gauges. The previously considered negligible contribution to the CMB radiation 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 flat as well as open universes is that lensing slightly smoothes the radiation power spectrum. For a given range of multipoles the effect of lensing increases with Omega but for the same acoustic peak it decreases with $\Omega$. The maximum contribution of lensing to the radiation power spectrum for $l\leq 2000$ is $\sim$ 5% for $\Omega$ values in the range 0.1-1.