Planck 2015 results

XIII. Cosmological parameters

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 MathematicalSciences, 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 Aix Marseille Université, Centre de Physique Théorique, 163 Avenue de Luminy, 13288 Marseille, France
⁷ Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
⁸ Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, 4000 Durban, South Africa
⁹ Atacama Large Millimeter/submillimeter Array, ALMA Santiago Central Offices, Alonso de Cordova 3107, Vitacura, Casilla 763 0355, Santiago, Chile
¹⁰ CGEE, SCS Qd 9, Lote C, Torre C, 4° andar, Ed. Parque Cidade Corporate, CEP 70308-200, Brasília, DF, Brazil
¹¹ CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
¹² CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
¹³ CRANN, Trinity College, Dublin, Ireland
¹⁴ California Institute of Technology, Pasadena, California, USA
¹⁵ Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹⁶ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
¹⁷ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, California, USA
¹⁸ Consejo Superior de Investigaciones Científicas (CSIC), 28049 Madrid, Spain
¹⁹ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
²⁰ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
²¹ Département de Physique Théorique, Université de Genève, 24, Quai E. Ansermet, 1211 Genève 4, Switzerland
²² Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
²³ Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain
²⁴ Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, 38100 Toronto, Ontario, Canada
²⁵ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²⁶ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²⁷ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles, CA 90089, USA
²⁸ Department of Physics and Astronomy, Johns Hopkins University, Bloomberg Center 435, 3400 N. Charles St., Baltimore, MD 21218, USA
²⁹ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
³⁰ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
³¹ Department of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USA
³² Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00560 Helsinki, Finland
³³ Department of Physics, Princeton University, Princeton, New Jersey, NJ 08540, USA
³⁴ Department of Physics, University of California, Berkeley, California, CA 94720, USA
³⁵ Department of Physics, University of California, One Shields Avenue, Davis, California, CA 93106, USA
³⁶ Department of Physics, University of California, Santa Barbara, California, USA
³⁷ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, IL 61801 USA
³⁸ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³⁹ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
⁴⁰ Dipartimento di Fisica, Università La Sapienza, P. le A. Moro 2, 00185 Roma, Italy
⁴¹ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, Italy
⁴² Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
⁴³ Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00185 Roma, Italy
⁴⁴ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 1165 Copenhagen, Denmark
⁴⁵ Discovery Center, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 1165 Copenhagen, Denmark
⁴⁶ European Southern Observatory, ESO Vitacura, Alonso de Cordova 3107, Vitacura, Casilla 19001, Santiago, Chile
⁴⁷ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, 28691 Madrid, Spain
⁴⁸ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴⁹ Gran Sasso Science Institute, INFN, viale F. Crispi 7, 67100 L’ Aquila, Italy
⁵⁰ HGSFP and University of Heidelberg, Theoretical Physics Department, Philosophenweg 16, 69120 Heidelberg, Germany
⁵¹ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, Pennsylvania, USA
⁵² Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00560 Helsinki, Finland
⁵³ INAF−Osservatorio Astrofisico di Catania, via S. Sofia 78, 95123 Catania, Italy
⁵⁴ INAF−Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35131 Padova, Italy
⁵⁵ INAF−Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
⁵⁶ INAF−Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, Trieste, Italy
⁵⁷ INAF/IASF Bologna, via Gobetti 101, Bologna, Italy
⁵⁸ INAF/IASF Milano, via E. Bassini 15, Milano, Italy
⁵⁹ INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁶⁰ INFN, Sezione di Ferrara, via Saragat 1, 44122 Ferrara, Italy
⁶¹ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁶² INFN, Sezione di Roma 2, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00185 Roma, Italy
⁶³ INFN/National Institute for Nuclear Physics, via Valerio 2, 34127 Trieste, Italy
⁶⁴ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Grenoble Alpes, IPAG; CNRS, IPAG, 38000 Grenoble, France
⁶⁵ ISDC, Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁶⁶ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁶⁷ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁶⁸ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁶⁹ Institut Néel, CNRS, Université Joseph Fourier Grenoble I, 25 rue des Martyrs, 38042 Grenoble, France
⁷⁰ Institut Universitaire de France, 103, bd Saint-Michel, 75005 Paris, France
⁷¹ Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay Cedex, France
⁷² Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, France
⁷³ Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, 52056 Aachen, Germany
⁷⁴ Institute for Space Sciences, 077125 Bucharest-Magurale, Romania
⁷⁵ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁷⁶ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0371 Oslo, Norway
⁷⁷ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain
⁷⁸ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁷⁹ Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
⁸⁰ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁸¹ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁸² Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
⁸³ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁸⁴ Kazan Federal University, 18 Kremlyovskaya St., 420008 Kazan, Russia
⁸⁵ LAL, Université Paris-Sud, CNRS/IN2P3, 91898 Orsay, France
⁸⁶ LERMA, CNRS, Observatoire de Paris, 61 Avenue de l’Observatoire, Paris, France
⁸⁷ Laboratoire AIM, IRFU/Service d’Astrophysique−CEA/DSM−CNRS−Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁸⁸ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁸⁹ Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁹⁰ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁹¹ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁹² Lebedev Physical Institute of the Russian Academy of Sciences, Astro Space Centre, 84/32 Profsoyuznaya st., 117997 Moscow, GSP-7, Russia
⁹³ Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, 10617 Taipei, Taiwan
⁹⁴ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁹⁵ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁹⁶ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁹⁷ Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland
⁹⁸ Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark
⁹⁹ Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 1165 Copenhagen, Denmark
¹⁰⁰ Nordita (Nordic Institute for Theoretical Physics), Roslagstullsbacken 23, 106 91 Stockholm, Sweden
¹⁰¹ Optical Science Laboratory, University College London, Gower Street, London, UK
¹⁰² Physics Department, Shahid Beheshti University, Tehran, Iran
¹⁰³ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
¹⁰⁴ SMARTEST Research Centre, Università degli Studi e-Campus, via Isimbardi 10, 22060 Novedrate (CO), Italy
¹⁰⁵ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
¹⁰⁶ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
¹⁰⁷ Sorbonne Université-UPMC, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
¹⁰⁸ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, 117997 Moscow, Russia
¹⁰⁹ Space Sciences Laboratory, University of California, Berkeley, California, USA
¹¹⁰ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
¹¹¹ Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USA
¹¹² Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
¹¹³ Sydney Institute for Astronomy, School of Physics A28, University of Sydney, NSW 2006, Australia
¹¹⁴ The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics,Stockholm University, AlbaNova, 106 91 Stockholm, Sweden
¹¹⁵ Theory Division, PH-TH, CERN, 1211 Geneva 23, Switzerland
¹¹⁶ UPMC Univ Paris 06, UMR 7095, 98bis boulevard Arago, 75014 Paris, France
¹¹⁷ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
¹¹⁸ Universities Space Research Association, Stratospheric Observatory for Infrared Astronomy, MS 232-11, Moffett Field, CA 94035, USA
¹¹⁹ University Observatory, Ludwig Maximilian University of Munich, Scheinerstrasse 1, 81679 Munich, Germany
¹²⁰ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 11071 Granada, Spain
¹²¹ University of Granada, Instituto Carlos I de Física Teórica y Computacional, 11071 Granada, Spain
¹²² University of Heidelberg, Institute for Theoretical Physics, Philosophenweg 16, 69120 Heidelberg, Germany
¹²³ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

^⋆ Corresponding author: G. Efstathiou, e-mail: gpe@ast.cam.ac.uk

Received: 6 February 2015
Accepted: 4 June 2016

Abstract

This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H₀ = (67.8 ± 0.9) km s^-1Mpc^-1, a matter density parameter Ω_m = 0.308 ± 0.012, and a tilted scalar spectral index with n_s = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of . These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find N_eff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value N_eff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to ∑ m_ν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with | Ω_K | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r_0.002< 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r_0.002 < 0.09 and disfavours inflationarymodels with a V(φ) ∝ φ² potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w = −1.006 ± 0.045, consistent with the expected value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundances for the best-fit Planck base ΛCDM cosmology are in excellent agreement with observations. We also constraints on annihilating dark matter and on possible deviations from the standard recombination history. In neither case do we find no evidence for new physics. The Planck results for base ΛCDM are in good agreement with baryon acoustic oscillation data and with the JLA sample of Type Ia supernovae. However, as in the 2013 analysis, the amplitude of the fluctuation spectrum is found to be higher than inferred from some analyses of rich cluster counts and weak gravitational lensing. We show that these tensions cannot easily be resolved with simple modifications of the base ΛCDM cosmology. Apart from these tensions, the base ΛCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.