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

TL;DR

This paper presents a detailed analysis of gravitational lensing effects on the CMB using Planck data, reconstructing the lensing potential map, measuring its power spectrum, and demonstrating its consistency with the ΛCDM model, thereby improving cosmological parameter constraints.

Contribution

First detection of CMB lensing at multiple frequencies with high significance, and a new method to reconstruct the lensing potential map from Planck data.

Findings

Lensing potential map correlates with large-scale structure tracers.

Lensing power spectrum agrees with ΛCDM predictions.

Improves constraints on curvature and reionization optical depth.

Abstract

On the arcminute angular scales probed by Planck, the CMB anisotropies are gently perturbed by gravitational lensing. Here we present a detailed study of this effect, detecting lensing independently in the 100, 143, and 217GHz frequency bands with an overall significance of greater than 25sigma. We use the temperature-gradient correlations induced by lensing to reconstruct a (noisy) map of the CMB lensing potential, which provides an integrated measure of the mass distribution back to the CMB last-scattering surface. Our lensing potential map is significantly correlated with other tracers of mass, a fact which we demonstrate using several representative tracers of large-scale structure. We estimate the power spectrum of the lensing potential, finding generally good agreement with expectations from the best-fitting LCDM model for the Planck temperature power spectrum, showing that this measurement at z=1100 correctly predicts the properties of the lower-redshift, later-time structures which source the lensing potential. When combined with the temperature power spectrum, our measurement provides degeneracy-breaking power for parameter constraints; it improves CMB-alone constraints on curvature by a factor of two and also partly breaks the degeneracy between the amplitude of the primordial perturbation power spectrum and the optical depth to reionization, allowing a measurement of the optical depth to reionization which is independent of large-scale polarization data. Discarding scale information, our measurement corresponds to a 4% constraint on the amplitude of the lensing potential power spectrum, or a 2% constraint on the RMS amplitude of matter fluctuations at z~2.