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

¹ APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/lrfu, Observatoire de Paris, Sorbonne Paris Cité, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France
² Aalto University Metsähovi Radio Observatory, , Metsähovintie 114, 02540 Kylmälä, Finland
³ African Institute for Mathematical Sciences, , 6-8 Melrose Road, Muizenberg, Cape Town, South Africa
⁴ Agenzia Spaziale Italiana Science Data Center, , via del Politecnico snc, 00133 Roma, Italy
⁵ Agenzia Spaziale Italiana, Viale Liegi 26, Roma, Italy
⁶ Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
⁷ Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, , Westville Campus, Private Bag X54001, 4000 Durban, South Africa
⁸ Atacama Large Millimeter/submillimeter Array, ALMA Santiago Central Offices, Alonso de Cordova 3107, Vitacura, Casilla 763 0355, Santiago, Chile
⁹ CITA, University ofToronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
¹⁰ CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
¹¹ California Institute of Technology, Pasadena, California, USA
¹² Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹³ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
¹⁴ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, California, USA
¹⁵ Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain
¹⁶ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁷ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
¹⁸ Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Genève 4, Switzerland
¹⁹ Departamento de Física Fundamental, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain
²⁰ Departamento de Física, Universidad de Oviedo, , Avda. Calvo Sotelo s/n, Oviedo, Spain
²¹ Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, Ontario, Canada
²² Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²³ Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA
²⁴ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²⁵ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, , Los Angeles, CA 90089, USA
²⁶ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²⁷ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
²⁸ Department of Physics, Carnegie Mellon University, , 5000 Forbes Ave, Pittsburgh, PA 15213, USA
²⁹ Department of Physics, Florida State University, , Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USA
³⁰ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland
³¹ Department of Physics, Princeton University, , Princeton, New Jersey, USA
³² Department of Physics, University of California, , Berkeley, California, USA
³³ Department of Physics, University of California, , One Shields Avenue, Davis, California, USA
³⁴ Department of Physics, University of California, , Santa Barbara, California, USA
³⁵ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
³⁶ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³⁷ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³⁸ Dipartimento di Fisica, Università La Sapienza, , P.le A. Moro 2, 00185 Roma, Italy
³⁹ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, Italy
⁴⁰ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
⁴¹ Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00133 Roma, Italy
⁴² Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁴³ Dpto. Astrofísica, Universidad de La Laguna (ULL), , 38206, La Laguna, Tenerife, Spain
⁴⁴ European Southern Observatory, ESO Vitacura, Alonso de Cordova 3107, Vitacura, Casilla 19001 Santiago, Chile
⁴⁵ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain
⁴⁶ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴⁷ Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Väisäläntie 20, 21500 Piikkiö, Finland
⁴⁸ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, Pennsylvania, USA
⁴⁹ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁵⁰ INAF − Osservatorio Astrofisico di Catania, , via S. Sofia 78, Catania, Italy
⁵¹ INAF − Osservatorio Astronomico di Padova, , Vicolo dell’Osservatorio 5, Padova, Italy
⁵² INAF − Osservatorio Astronomico di Roma, , via di Frascati 33, Monte Porzio Catone, Italy
⁵³ INAF − Osservatorio Astronomico di Trieste, , via G.B. Tiepolo 11, Trieste, Italy
⁵⁴ INAF Istituto di Radioastronomia, via P. Gobetti 101, 40129 Bologna, Italy
⁵⁵ INAF/IASF Bologna, via Gobetti 101, Bologna, Italy
⁵⁶ INAF/IASF Milano, via E. Bassini 15, Milano, Italy
⁵⁷ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁵⁸ INFN, Sezione di Roma 1, Università di Roma Sapienza, , P.le Aldo Moro 2, 00185 Roma, Italy
⁵⁹ IPAG:Institut de Planétologie et d’Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, France
⁶⁰ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁶¹ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁶² Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁶³ Institut Néel, CNRS, Université Joseph Fourier Grenoble I, 25 rue des Martyrs, Grenoble, France
⁶⁴ Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁶⁵ Institut d’Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, Orsay, France
⁶⁶ Institut d’Astrophysique de Paris, CNRS (UMR 7095), , 98bis boulevard Arago, 75014, Paris, France
⁶⁷ Institute for Space Sciences, Bucharest-Magurale, Romania
⁶⁸ Institute of Astronomy and Astrophysics, Academia Sinica, Taipei, Taiwan
⁶⁹ Institute of Astronomy, University of Cambridge, , Madingley Road, Cambridge CB3 0HA, UK
⁷⁰ Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
⁷¹ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, Tenerife, Spain
⁷² Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
⁷³ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁷⁴ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁷⁵ Kavli Institute for Cosmology Cambridge, , Madingley Road, Cambridge, CB3 0HA, UK
⁷⁶ LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
⁷⁷ LERMA, CNRS, Observatoire de Paris, 61 avenue de l’Observatoire, Paris, France
⁷⁸ Laboratoire AIM, IRFU/Service d’Astrophysique − CEA/DSM − CNRS − Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁷⁹ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁸⁰ Laboratoire de Physique Subatomique et de Cosmologie, Université Joseph Fourier Grenoble I, CNRS/IN2P3, Institut National Polytechnique de Grenoble, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁸¹ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁸² Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁸³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁸⁴ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁸⁵ MilliLab, VTT Technical Research Centre of Finland, , Tietotie 3, Espoo, Finland
⁸⁶ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁸⁷ Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark
⁸⁸ Observational Cosmology, Mail Stop 367-17, California Institute of Technology, Pasadena, CA 91125, USA
⁸⁹ Optical Science Laboratory, University College London, , Gower Street, London, UK
⁹⁰ SB-ITP-LPPC, EPFL, 1015 Lausanne, Switzerland
⁹¹ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁹² School of Physics and Astronomy, Cardiff University, , Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁹³ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁹⁴ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, 117997 Moscow, Russia
⁹⁵ Space Sciences Laboratory, University of California, , Berkeley, California, USA
⁹⁶ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
⁹⁷ Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USA
⁹⁸ Sub-Department of Astrophysics, University of Oxford, , Keble Road, Oxford OX1 3RH, UK
⁹⁹ Theory Division, PH-TH, CERN, 1211 Geneva 23, Switzerland
¹⁰⁰ UPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, France
¹⁰¹ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
¹⁰² University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, Granada, Spain
¹⁰³ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 21 March 2013
Accepted: 16 March 2014

Abstract

On the arcminute angular scales probed by Planck, the cosmic microwave background (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 217 GHz frequency bands with an overall significance of greater than 25σ. We use thetemperature-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 ΛCDM 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 root-mean-squared amplitude of matter fluctuations at z ~ 2.