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We investigate the effect of gravitational lensing by matter distribution in the universe on the cosmic microwave background polarization power spectra and temperature-polarization cross-correlation spectrum. As in the case of the temperature spectrum, gravitational lensing leads to a smoothing of narrow features and the enhancement of power on the damping tail of the power spectrum. Because the acoustic peaks in polarization spectra are narrower than in the temperature spectrum the smoothing effect is significantly larger and can reach up to 10% for l<1000 and even more above that. A qualitatively new feature is the generation of B type polarization even when only E is intrinsically present, such as in the case of pure scalar perturbations. This may be directly observed with Planck and other future small scale polarization experiments. The gravitational lensing effect is incorporated in the new version (2. 4) of the CMBFAST code.
Zaldarriaga et al. (Mon,) studied this question.