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On the arcminute angular scales probed by Planck, the CMB anisotropies aregently perturbed by gravitational lensing. Here we present a detailed study ofthis effect, detecting lensing independently in the 100, 143, and 217GHzfrequency bands with an overall significance of greater than 25sigma. We usethe temperature-gradient correlations induced by lensing to reconstruct a(noisy) map of the CMB lensing potential, which provides an integrated measureof the mass distribution back to the CMB last-scattering surface. Our lensingpotential map is significantly correlated with other tracers of mass, a factwhich we demonstrate using several representative tracers of large-scalestructure. We estimate the power spectrum of the lensing potential, findinggenerally good agreement with expectations from the best-fitting LCDM model forthe Planck temperature power spectrum, showing that this measurement at z=1100correctly predicts the properties of the lower-redshift, later-time structureswhich source the lensing potential. When combined with the temperature powerspectrum, our measurement provides degeneracy-breaking power for parameterconstraints; it improves CMB-alone constraints on curvature by a factor of twoand also partly breaks the degeneracy between the amplitude of the primordialperturbation power spectrum and the optical depth to reionization, allowing ameasurement of the optical depth to reionization which is independent oflarge-scale polarization data. Discarding scale information, our measurementcorresponds to a 4% constraint on the amplitude of the lensing potential powerspectrum, or a 2% constraint on the RMS amplitude of matter fluctuations atz~2.

Planck 2013 results. XVII. Gravitational lensing by large-scale structure