Planck 2013 results. XVI. 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, Metsähovintie 114, 02540 Kylmälä, Finland
³ African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg, 7950 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, 00198 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 of Toronto, 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), 28006 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, 33007 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, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USA
²⁹ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00014 Helsinki, Finland
³⁰ Department of Physics, Princeton University, Princeton, New Jersey, USA
³¹ Department of Physics, University of California, Berkeley, California, USA
³² Department of Physics, University of California, One Shields Avenue, Davis, California, USA
³³ Department of Physics, University of California, Santa Barbara, California, 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 Dipartimentodi 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, 00185 Roma, Italy
³⁸ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, Italy
³⁹ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
⁴⁰ Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00133 Roma, Italy
⁴¹ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁴² Dpto. Astrofísica, Universidad de La Laguna (ULL), 38206, La Laguna, Tenerife, Spain
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, Villanueva de la Cañada, 28691 Madrid, Spain
⁴⁵ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴⁶ Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Väisäläntie 20, 21500 Piikkiö, Finland
⁴⁷ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, Pennsylvania, USA
⁴⁸ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁴⁹ INAF – Osservatorio Astrofisico di Catania, via S. Sofia 78, 95123 Catania, Italy
⁵⁰ INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁵¹ INAF – Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
⁵² INAF – Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, Trieste, Italy
⁵³ INAF Istituto di Radioastronomia, via P. Gobetti 101, 40129 Bologna, Italy
⁵⁴ INAF/IASF Bologna, via Gobetti 101, 40129 Bologna, Italy
⁵⁵ INAF/IASF Milano, via E. Bassini 15, 20133 Milano, Italy
⁵⁶ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁵⁷ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁵⁸ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, France
⁵⁹ ISDC Data Centre for Astrophysics, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
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, 38042 Grenoble, France
⁶⁴ Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁶⁵ Institut d’Astrophysique Spatiale, CNRS UMR8617, Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, France
⁶⁶ Institut d’Astrophysique de Paris, CNRS UMR7095, 98bis Bd Arago, 75014 Paris, France
⁶⁷ Institute for Space Sciences, 077125 Bucharest-Magurale, Romania
⁶⁸ Institute of Astronomy and Astrophysics, Academia Sinica, 106 Taipei, Taiwan
⁶⁹ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁷⁰ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0315 Oslo, Norway
⁷¹ Instituto de Astrofísica de Canarias, C/vía Láctea s/n, 38200, La Laguna, Tenerife, Spain
⁷² Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁷³ Istituto di Fisica del Plasma, CNR-ENEA-EURATOM Association, via R. Cozzi 53, 20125 Milano, Italy
⁷⁴ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁷⁵ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
⁷⁶ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁷⁷ LAL, Université Paris-Sud, CNRS/IN2P3, 91405 Orsay, France
⁷⁸ LERMA, CNRS, Observatoire de Paris, 61 Avenue de l’Observatoire, 75014 Paris, France
⁷⁹ Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁸⁰ Laboratoire Traitement et Communication de l’Information, CNRS(UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁸¹ 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
⁸² Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁸³ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁸⁴ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁸⁵ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada
⁸⁶ MilliLab, VTT Technical Research Centre of Finland, Tietotie 3, 02044 Espoo, Finland
⁸⁷ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁸⁸ Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁸⁹ Observational Cosmology, Mail Stop 367-17, California Institute of Technology, Pasadena CA 91125, USA
⁹⁰ Optical Science Laboratory, University College London, Gower Street, London, UK
⁹¹ SB-ITP-LPPC, EPFL, 1015, Lausanne, Switzerland
⁹² SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁹³ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, UK
⁹⁴ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁹⁵ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, 117997 Moscow, Russia
⁹⁶ Space Sciences Laboratory, University of California, Berkeley, California, USA
⁹⁷ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
⁹⁸ Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USA
⁹⁹ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
¹⁰⁰ Theory Division, PH-TH, CERN, 1211, Geneva 23, Switzerland
¹⁰¹ UPMC Univ Paris 06, UMR7095, 98bis Boulevard Arago, 75014 Paris, France
¹⁰² Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
¹⁰³ Universities Space Research Association, Stratospheric Observatory for Infrared Astronomy, MS 232-11, Moffett Field CA 94035, USA
¹⁰⁴ University Observatory, Ludwig Maximilian University of Munich, Scheinerstrasse 1, 81679 Munich, Germany
¹⁰⁵ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18071 Granada, Spain
¹⁰⁶ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 28 March 2013
Accepted: 24 February 2014

Abstract

This paper presents the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the Planck spectra at high multipoles (ℓ ≳ 40) are extremely well described by the standard spatially-flat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the Planck data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be θ_∗ = (1.04147 ± 0.00062) × 10^-2, Ω_bh² = 0.02205 ± 0.00028, Ω_ch² = 0.1199 ± 0.0027, and n_s = 0.9603 ± 0.0073, respectively(note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H₀ = (67.3 ± 1.2) km s^-1 Mpc^-1, and a high value of the matter density parameter, Ω_m = 0.315 ± 0.017. These values are in tension with recent direct measurements of H₀ and the magnitude-redshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using Planck CMB data alone. We use high-resolution CMB data together with Planck to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter ΛCDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured over the standard six-parameter ΛCDM cosmology. The deviation of the scalar spectral index from unity isinsensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r_0.002< 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find N_eff = 3.30 ± 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of N_eff = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = -1.13_-0.10^+0.13. We also use the Planck data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter ΛCDM model in describing the Planck data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. The unusual shape of the spectrum in the multipole range 20 ≲ ℓ ≲ 40 was seen previously in the WMAP data and is a real feature of the primordial CMB anisotropies. The poor fit to the spectrum at low multipoles is not of decisive significance, but is an “anomaly” in an otherwise self-consistent analysis of the Planck temperature data.