Planck 2018 results

VI. Cosmological parameters

¹ AIM, CEA, CNRS, Université Paris-Saclay, Université Paris-Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
² 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
³ African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg, Cape Town, South Africa
⁴ Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
⁵ Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge, CB3 0HE, UK
⁶ Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa
⁷ CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
⁸ CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
⁹ Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
¹⁰ California Institute of Technology, Pasadena, California, USA
¹¹ Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹² Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
¹³ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
¹⁴ Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Genève 4, Switzerland
¹⁵ Département de Physique, École normale supérieure, PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
¹⁶ Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
¹⁷ Departamento de Física, Universidad de Oviedo, C/ Federico García Lorca, 18, Oviedo, Spain
¹⁸ Department of Astrophysics/IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, The Netherlands
¹⁹ Department of Mathematics, University of Stellenbosch, Stellenbosch 7602, South Africa
²⁰ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC, Canada
²¹ Department of Physics & Astronomy, University of the Western Cape, Cape Town 7535, South Africa
²² Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²³ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
²⁴ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland
²⁵ Department of Physics, Princeton University, Princeton, NJ, USA
²⁶ Department of Physics, University of California, Berkeley, CA, USA
²⁷ Department of Physics, University of California, One Shields Avenue, Davis, CA, USA
²⁸ Department of Physics, University of California, Santa Barbara, CA, USA
²⁹ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³⁰ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
³¹ Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, Roma, Italy
³² Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy
³³ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, Trieste, Italy
³⁴ Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, Roma, Italy
³⁵ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain
³⁶ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ, Noordwijk, The Netherlands
³⁷ Gran Sasso Science Institute, INFN, viale F. Crispi 7, 67100 L’Aquila, Italy
³⁸ HEP Division, Argonne National Laboratory, Lemont, IL 60439, USA
³⁹ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, PA, USA
⁴⁰ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁴¹ INAF – OAS Bologna, Istituto Nazionale di Astrofisica – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Area della Ricerca del CNR, Via Gobetti 101, 40129 Bologna, Italy
⁴² INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, Italy
⁴³ INAF – Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, Italy
⁴⁴ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
⁴⁵ INAF/IASF Milano, Via E. Bassini 15, Milano, Italy
⁴⁶ INFN – CNAF, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁷ INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁸ INFN, Sezione di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
⁴⁹ INFN, Sezione di Milano, Via Celoria 16, Milano, Italy
⁵⁰ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁵¹ INFN, Sezione di Roma 2, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, Roma, Italy
⁵² IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, Pune 411 007, India
⁵³ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK
⁵⁴ Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay Cedex, France
⁵⁵ Institut d’Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France
⁵⁶ Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, 52056 Aachen, Germany
⁵⁷ Institute Lorentz, Leiden University, PO Box 9506, Leiden 2300 RA, The Netherlands
⁵⁸ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁵⁹ Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
⁶⁰ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, Tenerife, Spain
⁶¹ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
⁶² Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
⁶³ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
⁶⁴ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
⁶⁵ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶⁶ Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), UTIAS, The University of Tokyo, Chiba 277- 8583, Japan
⁶⁷ Laboratoire d’Océanographie Physique et Spatiale (LOPS), Univ. Brest, CNRS, Ifremer, IRD, Brest, France
⁶⁸ Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁶⁹ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁷⁰ Lawrence Berkeley National Laboratory, Berkeley, CA, USA
⁷¹ Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, 00076 Aalto, Finland
⁷² Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁷³ Mullard Space Science Laboratory, University College London, Surrey RH5 6NT, UK
⁷⁴ NAOC-UKZN Computational Astrophysics Centre (NUCAC), University of KwaZulu-Natal, Durban 4000, South Africa
⁷⁵ National Centre for Nuclear Research, ul. L. Pasteura 7, 02-093 Warsaw, Poland
⁷⁶ Physics Department, Shahid Beheshti University, Velenjak, Tehran 19839, Iran
⁷⁷ Purple Mountain Observatory, No. 8 Yuan Hua Road, 210034 Nanjing, PR China
⁷⁸ SISSA, Astrophysics Sector, Via Bonomea 265, 34136 Trieste, Italy
⁷⁹ San Diego Supercomputer Center, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
⁸⁰ School of Chemistry and Physics, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa
⁸¹ School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni, 752050 Odissa, India
⁸² School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, UK
⁸³ School of Physics and Astronomy, Sun Yat-sen University, 2 Daxue Rd, Tangjia, Zhuhai, PR China
⁸⁴ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁸⁵ School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Maruthamala PO, Vithura, Thiruvananthapuram 695551, Kerala, India
⁸⁶ School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia
⁸⁷ Simon Fraser University, Department of Physics, 8888 University Drive, Burnaby, BC, Canada
⁸⁸ Sorbonne Université, Institut Lagrange de Paris (ILP), 98bis boulevard Arago, 75014 Paris, France
⁸⁹ Sorbonne Université, Observatoire de Paris, Université PSL, École normale supérieure, CNRS, LERMA, 75005 Paris, France
⁹⁰ Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
⁹¹ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, Moscow 117997, Russia
⁹² Space Science Data Center – Agenzia Spaziale Italiana, Via del Politecnico snc, 00133 Roma, Italy
⁹³ Space Sciences Laboratory, University of California, Berkeley, CA, USA
⁹⁴ The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova 106 91, Stockholm, Sweden
⁹⁵ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
⁹⁶ University of Heidelberg, Institute for Theoretical Physics, Philosophenweg 16, 69120 Heidelberg, Germany
⁹⁷ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 20 July 2018
Accepted: 20 March 2020

Abstract

We present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ω_ch² = 0.120 ± 0.001, baryon density Ω_bh² = 0.0224 ± 0.0001, scalar spectral index n_s = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ_* = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H₀ = (67.4 ± 0.5)  km s⁻¹ Mpc⁻¹; matter density parameter Ω_m = 0.315 ± 0.007; and matter fluctuation amplitude σ₈ = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be N_eff = 2.99 ± 0.17, in agreement with the Standard Model prediction N_eff = 3.046, and find that the neutrino mass is tightly constrained to ∑m_ν <  0.12  eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, Ω_K = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w₀ = −1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r_0.002 <  0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6σ, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.