Planck 2018 results

V. CMB power spectra and likelihoods

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, 4000 Durban, 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, CA, 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, One Shields Avenue, Davis, CA, USA
²⁷ Department of Physics, University of California, Santa Barbara, CA, USA
²⁸ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, Via Marzolo 8, 35131 Padova, Italy
²⁹ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
³⁰ Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, Roma, Italy
³¹ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy
³² Dipartimento di Fisica, Università degli Studi di Trieste, Via A. Valerio 2, Trieste, Italy
³³ Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, Roma, Italy
³⁴ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain
³⁵ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
³⁶ Gran Sasso Science Institute, INFN, Viale F. Crispi 7, 67100 L’Aquila, Italy
³⁷ HEP Division, Argonne National Laboratory, Lemont, IL 60439, USA
³⁸ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, PA, USA
³⁹ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁴⁰ IFPU – Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
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 – Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
⁴⁵ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
⁴⁶ INAF/IASF Milano, Via E. Bassini 15, Milano, Italy
⁴⁷ INFN – CNAF, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁸ INFN, Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁹ INFN, Sezione di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
⁵⁰ INFN, Sezione di Milano, Via Celoria 16, Milano, Italy
⁵¹ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁵² INFN, Sezione di Roma 2, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, Roma, Italy
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 Institute Lorentz, Leiden University, PO Box 9506, 2300 RA Leiden, The Netherlands
⁵⁷ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁵⁸ Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
⁵⁹ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, Tenerife, Spain
⁶⁰ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
⁶¹ Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
⁶² Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
⁶³ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
⁶⁴ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶⁵ Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), UTIAS, The University of Tokyo, Chiba 277-8583, Japan
⁶⁶ Laboratoire d’Océanographie Physique et Spatiale (LOPS), Univ. Brest, CNRS, Ifremer, IRD, Brest, France
⁶⁷ Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁶⁸ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁶⁹ Lawrence Berkeley National Laboratory, Berkeley, CA, USA
⁷⁰ Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo 00076 Aalto, Finland
⁷¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁷² Mullard Space Science Laboratory, University College London, Surrey RH5 6NT, UK
⁷³ NAOC-UKZN Computational Astrophysics Centre (NUCAC), University of KwaZulu-Natal, 4000 Durban, South Africa
⁷⁴ National Centre for Nuclear Research, ul. L. Pasteura 7, 02-093 Warsaw, Poland
⁷⁵ Purple Mountain Observatory, No. 8 Yuan Hua Road, 210034 Nanjing, PR China
⁷⁶ SISSA, Astrophysics Sector, Via Bonomea 265, 34136 Trieste, Italy
⁷⁷ San Diego Supercomputer Center, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
⁷⁸ School of Chemistry and Physics, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, 4000 Durban, South Africa
⁷⁹ School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni 752050, Odissa, India
⁸⁰ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, UK
⁸¹ School of Physics and Astronomy, Sun Yat-sen University, 2 Daxue Rd, Tangjia, Zhuhai, PR China
⁸² School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁸³ School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Maruthamala PO, Vithura, Thiruvananthapuram 695551, Kerala, India
⁸⁴ School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia
⁸⁵ Simon Fraser University, Department of Physics, 8888 University Drive, Burnaby, BC, Canada
⁸⁶ Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98bis bd Arago, 75014 Paris, France
⁸⁷ Sorbonne Université, Institut Lagrange de Paris (ILP), 98bis boulevard Arago, 75014 Paris, France
⁸⁸ Sorbonne Université, Observatoire de Paris, Université PSL, École normale supérieure, CNRS, LERMA, 75005 Paris, France
⁸⁹ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, Moscow 117997, Russia
⁹⁰ Space Science Data Center – Agenzia Spaziale Italiana, Via del Politecnico snc, 00133 Roma, Italy
⁹¹ Space Sciences Laboratory, University of California, Berkeley, CA, USA
⁹² The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova 106 91, Stockholm, Sweden
⁹³ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
⁹⁴ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 25 July 2019
Accepted: 25 May 2020

Abstract

We describe the legacy Planck cosmic microwave background (CMB) likelihoods derived from the 2018 data release. The overall approach is similar in spirit to the one retained for the 2013 and 2015 data release, with a hybrid method using different approximations at low (ℓ <  30) and high (ℓ ≥ 30) multipoles, implementing several methodological and data-analysis refinements compared to previous releases. With more realistic simulations, and better correction and modelling of systematic effects, we can now make full use of the CMB polarization observed in the High Frequency Instrument (HFI) channels. The low-multipole EE cross-spectra from the 100 GHz and 143 GHz data give a constraint on the ΛCDM reionization optical-depth parameter τ to better than 15% (in combination with the TT low-ℓ data and the high-ℓ temperature and polarization data), tightening constraints on all parameters with posterior distributions correlated with τ. We also update the weaker constraint on τ from the joint TEB likelihood using the Low Frequency Instrument (LFI) channels, which was used in 2015 as part of our baseline analysis. At higher multipoles, the CMB temperature spectrum and likelihood are very similar to previous releases. A better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (i.e., the polarization efficiencies) allow us to make full use of polarization spectra, improving the ΛCDM constraints on the parameters θ_MC, ω_c, ω_b, and H₀ by more than 30%, and n_s by more than 20% compared to TT-only constraints. Extensive tests on the robustness of the modelling of the polarization data demonstrate good consistency, with some residual modelling uncertainties. At high multipoles, we are now limited mainly by the accuracy of the polarization efficiency modelling. Using our various tests, simulations, and comparison between different high-multipole likelihood implementations, we estimate the consistency of the results to be better than the 0.5 σ level on the ΛCDM parameters, as well as classical single-parameter extensions for the joint likelihood (to be compared to the 0.3 σ levels we achieved in 2015 for the temperature data alone on ΛCDM only). Minor curiosities already present in the previous releases remain, such as the differences between the best-fit ΛCDM parameters for the ℓ <  800 and ℓ >  800 ranges of the power spectrum, or the preference for more smoothing of the power-spectrum peaks than predicted in ΛCDM fits. These are shown to be driven by the temperature power spectrum and are not significantly modified by the inclusion of the polarization data. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations.