Planck 2018 results
Astronomy and Astrophysics, vol. 652, pp. C4
Abstract
In the original version, the bounds given in Eqs. (87a) and (87b) on the contribution to the early-time optical depth, (15,30), contained a numerical error in deriving the 95th percentile from the Monte Carlo samples. The corrected 95% upper bounds are: τ(15,30) < 0:018 (lowE, flat τ(15, 30), FlexKnot), (1) τ(15, 30) < 0:023 (lowE, flat knot, FlexKnot): (2) These bounds are a factor of 3 larger than the originally reported results. Consequently, the new bounds do not significantly improve upon previous results from Planck data presented in Millea & Bouchet (2018) as was stated, but are instead comparable. Equations (1) and (2) give results that are now similar to those of Heinrich & Hu (2021), who used the same Planck 2018 data to derive a 95% upper bound of 0.020 using the principal component analysis (PCA) model and uniform priors on the PCA mode amplitudes.
Authors 96
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Université Paris-Sud · Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut d'Astrophysique Spatiale
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Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay cedex, France
Institut d'Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay cedex, France
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Leiden University · Centre National de la Recherche Scientifique · University of Oslo · Université Paris Sciences et Lettres · École Normale Supérieure - PSL
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Département de Physique, École normale supérieure, PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
Institute Lorentz, Leiden University, PO Box 9506 Leiden 2300 RA, The Netherlands
Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
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Affiliation as printed
Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
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Université Toulouse III - Paul Sabatier · Institut de Recherche en Astrophysique et Planétologie · Université de Toulouse
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Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse cedex 4, France
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Scuola Internazionale Superiore di Studi Avanzati
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SISSA, Astrophysics Sector, Via Bonomea 265, 34136 Trieste, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · University of the Western Cape · National Institute for Astrophysics
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Department of Physics & Astronomy, University of the Western Cape, Cape Town 7535, South Africa
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
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Centre National de la Recherche Scientifique · Université Toulouse III - Paul Sabatier · Institut de Recherche en Astrophysique et Planétologie · Université de Toulouse
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CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse cedex 4, France
Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse cedex 4, France
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Universidad de Cantabria · Instituto de Física de Cantabria
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Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
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University of Padua · Istituto Nazionale di Fisica Nucleare, Sezione di Padova
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Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, Via Marzolo 8, 35131 Padova, Italy
Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
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Indian Institute of Science Education and Research Thiruvananthapuram
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School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Maruthamala PO, Vithura, Thiruvananthapuram, 695551 Kerala, India
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Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
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Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université
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Institut d’Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
Institut d'Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
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Centre National de la Recherche Scientifique · Université Toulouse III - Paul Sabatier · Institut de Recherche en Astrophysique et Planétologie · Université de Toulouse
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CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse cedex 4, France
Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse cedex 4, France
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University of Milan · National Institute for Astrophysics
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Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy
INAF/IASF Milano, Via E. Bassini 15, Milano, Italy
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Scuola Internazionale Superiore di Studi Avanzati · National Centre for Nuclear Research
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National Centre for Nuclear Research, ul. L. Pasteura 7, 02-093 Warsaw, Poland
SISSA, Astrophysics Sector, Via Bonomea 265, 34136 Trieste, Italy
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California Institute of Technology · Jet Propulsion Laboratory
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California Institute of Technology, Pasadena, CA, USA
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
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University of Toronto · Canadian Institute for Theoretical Astrophysics
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CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
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Lawrence Berkeley National Laboratory · Space Sciences Laboratory · University of California, Berkeley
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Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université
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Institut d’Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
Institut d'Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
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Université Paris-Sud · Centre National de la Recherche Scientifique · Université Paris Sciences et Lettres · Université Paris-Saclay · Observatoire de Paris · Institut d'Astrophysique de Paris · Sorbonne Université · Institut d'Astrophysique Spatiale · Laboratoire d’Etudes du Rayonnement et de la Matière en Astrophysique et Atmosphères
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Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay cedex, France
Institut d’Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, Observatoire de Paris, Université PSL, École normale supérieure, CNRS, LERMA, 75005 Paris, France
Institut d'Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay cedex, France
Institut d'Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
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Centre National de la Recherche Scientifique · Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Observatoire de Paris · Laboratoire AstroParticule et Cosmologie · Sorbonne Paris Cité · Institut National de Physique Nucléaire et de Physique des Particules · Université Paris Diderot · University of KwaZulu-Natal
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Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa
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University of Ferrara · Istituto di Radioastronomia di Bologna · Istituto Nazionale di Fisica Nucleare, Sezione di Bologna
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université
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Institut d’Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
Institut d'Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
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Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
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Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
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Princeton University · University of KwaZulu-Natal
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Department of Physics, Princeton University, Princeton, NJ, USA
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Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
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Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy
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Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Laboratoire de Physique Subatomique et de Cosmologie · Université Grenoble Alpes
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University of British Columbia
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California Institute of Technology · Jet Propulsion Laboratory
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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Centre National de la Recherche Scientifique · Ifremer · Laboratory for Ocean Physics and Satellite Remote Sensing · Institut de Recherche pour le Développement
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Universidad de Cantabria · Instituto de Física de Cantabria
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Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
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California Institute of Technology · Jet Propulsion Laboratory
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Université Paris-Sud · Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut d'Astrophysique Spatiale
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Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay cedex, France
Institut d'Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay cedex, France
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Kavli Institute for the Physics and Mathematics of the Universe · The University of Tokyo
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Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), UTIAS, The University of Tokyo, Chiba 277- 8583, Japan
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European Space Agency · European Space Astronomy Centre
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European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain
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Istituto Nazionale di Fisica Nucleare, Sezione di Padova
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Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
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Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
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Max Planck Institute for Astrophysics
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Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
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Max Planck Institute for Astrophysics
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Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
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Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
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African Institute for Mathematical Sciences · Stellenbosch University
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African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg, Cape Town, South Africa
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Physics Department, Shahid Beheshti University, Velenjak, Tehran 19839, Iran
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Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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Universidad de Cantabria · Instituto de Física de Cantabria
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Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
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Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INFN, Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
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University of Ferrara · Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara
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Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
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Trieste Astronomical Observatory
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Department of Physics, Princeton University, Princeton, NJ, USA
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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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
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Trieste Astronomical Observatory
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Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université
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Institut d’Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
Institut d'Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
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Centre National de la Recherche Scientifique · Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Observatoire de Paris · Laboratoire AstroParticule et Cosmologie · Sorbonne Paris Cité · Institut National de Physique Nucléaire et de Physique des Particules · Université Paris Diderot
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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
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Universidad de La Laguna · Instituto de Astrofísica de Canarias
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HEP Division, Argonne National Laboratory, Lemont, IL 60439, USA
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California Institute of Technology · National Institute of Science Education and Research
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Departamento de Física, Universidad de Oviedo, C/ Federico García Lorca, 18, Oviedo, Spain
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California Institute of Technology · Jet Propulsion Laboratory · University of Warsaw
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Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
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Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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Stockholm University · Princeton University · AlbaNova
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Department of Physics, Princeton University, Princeton, NJ, USA
The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, 106 91 Stockholm, Sweden
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School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia
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Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
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Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
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Universidad de Cantabria · Instituto de Física de Cantabria
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Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
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California Institute of Technology · Jet Propulsion Laboratory
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Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université
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Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
Institut d'Astrophysique de Paris, CNRS (UMR7095), 98 bis Boulevard Arago, 75014 Paris, France
Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
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School of Physics and Astronomy, Sun Yat-sen University, 2 Daxue Rd, Tangjia, Zhuhai, PR China
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Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK
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Department of Physics, Princeton University, Princeton, NJ, USA
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Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
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Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland
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Lawrence Berkeley National Laboratory
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Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
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University of Helsinki · Helsinki Institute of Physics
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Max Planck Institute for Astrophysics
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Lawrence Berkeley National Laboratory
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University of California, Davis
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Scuola Internazionale Superiore di Studi Avanzati
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Université Paris-Sud · University of Geneva · Centre National de la Recherche Scientifique · African Institute for Mathematical Sciences · Université Paris-Saclay · Institut d'Astrophysique Spatiale
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African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg, Cape Town, South Africa
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Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay cedex, France
Institut d'Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay cedex, France
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University of Helsinki · Helsinki Institute of Physics
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Centre National de la Recherche Scientifique · Aix-Marseille Université
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Sorbonne Université, Observatoire de Paris, Université PSL, École normale supérieure, CNRS, LERMA, 75005 Paris, France
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Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
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University of Ferrara · Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara
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Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
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California Institute of Technology · Jet Propulsion Laboratory
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Centre National de la Recherche Scientifique · Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Observatoire de Paris · Laboratoire AstroParticule et Cosmologie · Sorbonne Paris Cité · Institut National de Physique Nucléaire et de Physique des Particules · Université Paris Diderot
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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
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Affiliation as printed
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
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Centre National de la Recherche Scientifique · Université Paris Sciences et Lettres · Observatoire de Paris · Sorbonne Université · Laboratoire d’Etudes du Rayonnement et de la Matière en Astrophysique et Atmosphères
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Sorbonne Université, Observatoire de Paris, Université PSL, École normale supérieure, CNRS, LERMA, 75005 Paris, France
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Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
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University of Padua · Istituto Nazionale di Fisica Nucleare, Sezione di Padova
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Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, Via Marzolo 8, 35131 Padova, Italy
Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
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