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Weak lensing of the CMB changes the unlensed temperature anisotropy and polarization power spectra. Accounting for the lensing effect will be crucial to obtain accurate parameter constraints from sensitive CMB observations. Methods for computing the lensed power spectra using a low-order perturbative expansion are not good enough for percent-level accuracy. Nonperturbative flat-sky methods are more accurate, but curvature effects change the spectra at the 0. 3%--1% level. We describe a new, accurate, and fast, full-sky correlation-function method for computing the lensing effect on CMB power spectra to better than 0. 1% at l2500 (within the approximation that the lensing potential is linear and Gaussian). We also discuss the effect of nonlinear evolution of the gravitational potential on the lensed power spectra. Our fast numerical code is publicly available.
Challinor et al. (2005) studied this question.