Gravitational lensing effect on cosmic microwave background anisotropies: A power spectrum approach

The effect of gravitational lensing on cosmic microwave background (CMB) anisotropies is investigated using the power spectrum approach. The lensing effect can be calculated in any cosmological model by specifying the evolution of gravitational potential. Previous work on this subject is generalized to a nonflat universe and to a nonlinear evolution regime. Gravitational lensing cannot change the gross distribution of CMB anisotropies, but it may redistribute the power and smooth the sharp features in the CMB power spectrum. The magnitude of this effect is estimated using observational constraints on the power spectrum of gravitational potential from galaxy and cluster surveys and also using the limits on correlated ellipticities in distant galaxies. For realistic CMB power spectra the effect on CMB multipole moments is less than a few percent on degree angular scales but gradually increases toward smaller scales. On arcminute angular scales the acoustic oscillation peaks may be partially or completely smoothed out because of the gravitational lensing.