Lensing effect on polarization in the microwave background: Extracting the convergence power spectrum

Matter inhomogeneities along the line of sight deflect the cosmic microwave background (CMB) photons originating at the last scattering surface at a redshift $z\sim 1100.$ These distortions modify the pattern of CMB polarization. We identify specific combinations of Stokes Q and U parameters that correspond to spin 0, ±2 variables and can be used to reconstruct the projected matter density. We compute the expected signal-to-noise ratio as a function of detector sensitivity and angular resolution. With the Planck satellite the detection would be at a few $\sigma$ level. Several times better detector sensitivity would be needed to measure the projected dark matter power spectrum over a wider range of scales, which could provide an independent confirmation of the projected matter power spectrum as measured from other methods.