Planck 2015 results

XV. Gravitational lensing

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 and Dept of Radio Science and Engineering, PO Box 13000, 00076 AALTO, Finland
³ African Institute for Mathematical Sciences, 6–8 Melrose Road, Muizenberg, 7945 Cape Town, South Africa
⁴ Agenzia Spaziale Italiana Science Data Center, via del Politecnico snc, 00133 Roma, Italy
⁵ Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille), UMR 7326, 13388 Marseille, France
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, Durban 4000, South Africa
⁸ Atacama Large Millimeter/submillimeter Array, ALMA Santiago Central Offices, Alonso de Cordova 3107, Vitacura, Casilla 763 0355, Santiago, Chile
⁹ CGEE, SCS Qd 9, Lote C, Torre C, 4° andar, Ed. Parque Cidade Corporate, CEP 70308-200, Brasília, DF, Brazil
¹⁰ CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
¹¹ CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
¹² CRANN, Trinity College, Dublin 2, Ireland
¹³ California Institute of Technology, Pasadena, CA 91125 California, USA
¹⁴ Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹⁵ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
¹⁶ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 California, USA
¹⁷ Consejo Superior de Investigaciones Científicas (CSIC), 28006 Madrid, Spain
¹⁸ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁹ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
²⁰ Département de Physique Théorique, Université de Genève, 24, Quai E. Ansermet, 1211 Genève 4, Switzerland
²¹ Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
²² Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33003 Oviedo, Spain
²³ Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, Ontario ONMSR 0A3, Canada
²⁴ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²⁵ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver BC V6T 1Z4, British Columbia, Canada
²⁶ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles, CA 90089, USA
²⁷ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²⁸ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
²⁹ Department of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida FL 32306, USA
³⁰ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00100 Helsinki, Finland
³¹ Department of Physics, Princeton University, Princeton, New Jersey NJ 08544, USA
³² Department of Physics, University of California, Berkeley, California CA 93106, USA
³³ Department of Physics, University of California, Santa Barbara, California CA 93106, USA
³⁴ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
³⁵ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³⁶ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³⁷ Dipartimento di Fisica, Università La Sapienza, P. le A. Moro 2, Roma, Italy
³⁸ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, Milano, Italy
³⁹ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, Trieste, Italy
⁴⁰ Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, Roma, Italy
⁴¹ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark
⁴² Discovery Center, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, Copenhagen, Denmark
⁴³ European Southern Observatory, ESO Vitacura, Alonso de Cordova 3107, Vitacura, Casilla 19001, Santiago, Chile
⁴⁴ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁴⁵ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴⁶ Facoltà di Ingegneria, Università degli Studi e-Campus, via Isimbardi 10, 22060 Novedrate (CO), Italy
⁴⁷ Gran Sasso Science Institute, INFN, viale F. Crispi 7, 67100 L’ Aquila, Italy
⁴⁸ HGSFP and University of Heidelberg, Theoretical Physics Department, Philosophenweg 16, 69120 Heidelberg, Germany
⁴⁹ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00100 Helsinki, Finland
⁵⁰ INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35141 Padova, Italy
⁵¹ INAF–Osservatorio Astronomico di Roma, via di Frascati 33, Monte Porzio Catone, 00136 Roma, Italy
⁵² INAF–Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34131 Trieste, Italy
⁵³ INAF/IASF Bologna, via Gobetti 101, 40127 Bologna, Italy
⁵⁴ INAF/IASF Milano, via E. Bassini 15, 28 Milano, Italy
⁵⁵ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁵⁶ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁵⁷ INFN, Sezione di Roma 2, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1 Roma, Italy
⁵⁸ INFN/National Institute for Nuclear Physics, via Valerio 2, 34127 Trieste, Italy
⁵⁹ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Grenoble Alpes, IPAG, 38000 Grenoble, France
⁶⁰ CNRS, IPAG, 38000 Grenoble, France
⁶¹ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁶² Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁶³ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁶⁴ Institut Néel, CNRS, Université Joseph Fourier Grenoble I, 25 rue des Martyrs, 38401 Saint-Martin-d’Hères, Grenoble, France
⁶⁵ Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁶⁶ Institut d’Astrophysique Spatiale, CNRS (UMR8617) Université Paris-Sud 11, Bâtiment 121, 91400 Orsay, France
⁶⁷ Institut d’Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
⁶⁸ Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, 52056 Aachen, Germany
⁶⁹ Institute for Space Sciences, 077125 Bucharest-Magurale, Romania
⁷⁰ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁷¹ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0316 Oslo, Norway
⁷² Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, 38205 Tenerife, Spain
⁷³ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
⁷⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
⁷⁵ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California CA 91125, USA
⁷⁶ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁷⁷ Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
⁷⁸ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁷⁹ Kazan Federal University, 18 Kremlyovskaya St., 420008 Kazan, Russia
⁸⁰ LAL, Université Paris-Sud, CNRS/IN2P3, 91400 Orsay, France
⁸¹ LERMA, CNRS, Observatoire de Paris, 61 Avenue de l’Observatoire, 75014 Paris, France
⁸² Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁸³ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁸⁴ Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁸⁵ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁸⁶ Lawrence Berkeley National Laboratory, Berkeley, California CA 94720, USA
⁸⁷ Lebedev Physical Institute of the Russian Academy of Sciences, Astro Space Centre, 84/32 Profsoyuznaya st., 117997 Moscow, GSP-7, Russia
⁸⁸ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁸⁹ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁹⁰ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁹¹ Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland
⁹² Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁹³ Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁹⁴ Nordita (Nordic Institute for Theoretical Physics), Roslagstullsbacken 23, 106 91 Stockholm, Sweden
⁹⁵ Optical Science Laboratory, University College London, Gower Street, London WC1E 6BT, UK
⁹⁶ SISSA, Astrophysics Sector, via Bonomea 265, 34136, Trieste, Italy
⁹⁷ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁹⁸ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁹⁹ Sorbonne Université-UPMC, UMR7095, Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
¹⁰⁰ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, 117997 Moscow, Russia
¹⁰¹ Space Sciences Laboratory, University of California, Berkeley, California, USA
¹⁰² Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
¹⁰³ Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California CA 94305, USA
¹⁰⁴ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
¹⁰⁵ The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, 106 91 Stockholm, Sweden
¹⁰⁶ Theory Division, PH-TH, CERN, 1211, Geneva 23, Switzerland
¹⁰⁷ UPMC Univ Paris 06, UMR7095, 98 bis Boulevard Arago, 75014 Paris, France
¹⁰⁸ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
¹⁰⁹ Universities Space Research Association, Stratospheric Observatory for Infrared Astronomy, MS 232-11, Moffett Field, CA 94035, USA
¹¹⁰ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18010 Granada, Spain
¹¹¹ University of Granada, Instituto Carlos I de Física Teórica y Computacional, 18010 Granada, Spain
¹¹² Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

^⋆ Corresponding author: D. Hanson, e-mail: duncan.hanson@gmail.com

Received: 23 February 2015
Accepted: 15 December 2015

Abstract

We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40σ), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator, we detect lensing at a significance of 5σ. We cross-check the accuracy of our measurement using the wide frequency coverage and complementarity of the temperature and polarization measurements. Public products based on this measurement include an estimate of the lensing potential over approximately 70% of the sky, an estimate of the lensing potential power spectrum in bandpowers for the multipole range 40 ≤ L ≤ 400, and an associated likelihood for cosmological parameter constraints. We find good agreement between our measurement of the lensing potential power spectrum and that found in the ΛCDM model that best fits the Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percent-level measurement of the parameter combination σ₈Ω^0.25_m = 0.591 ± 0.021. We combine our determination of the lensing potential with the E-mode polarization, also measured by Planck, to generate an estimate of the lensing B-mode. We show that this lensing B-mode estimate is correlated with the B-modes observed directly by Planck at the expected level and with a statistical significance of 10σ, confirming Planck’s sensitivity to this known sky signal. We also correlate our lensing potential estimate with the large-scale temperature anisotropies, detecting a cross-correlation at the 3σ level, as expected because of dark energy in the concordance ΛCDM model.