Planck 2018 results

Astronomy and Astrophysics, vol. 641, pp. A9

Abstract

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E -mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: f NL local = −0.9 ± 5.1; f NL equil = −26 ± 47; and f NL ortho = −38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 σ . Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is g NL local = (−5.8 ± 6.5) × 10 4 (68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

Authors 98

1. Y. Akrami Aachen Institute Lorentz

   Leiden University · Centre National de la Recherche Scientifique · University of Oslo · Université Paris Sciences et Lettres · École Normale Supérieure - PSL

   Affiliation as printed

   Département de Physique, École normale supérieure, PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France

   Institute Lorentz, Leiden University, PO Box 9506, 2300 RA Leiden, The Netherlands

   Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway

2. Frederico Arroja

   University of Lisbon · Institute of Astrophysics and Space Sciences

   Affiliation as printed

   Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal

3. M. Ashdown

   University of Cambridge

   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

4. J. Aumont

   Université Toulouse III - Paul Sabatier · Institut de Recherche en Astrophysique et Planétologie · Université de Toulouse

   Affiliation as printed

   Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France

5. Carlo Baccigalupi

   Scuola Internazionale Superiore di Studi Avanzati

   Affiliation as printed

   SISSA, Astrophysics Sector, Via Bonomea 265, 34136 Trieste, Italy

6. M. Ballardini

   Osservatorio di Astrofisica e Scienza dello Spazio · University of the Western Cape · National Institute for Astrophysics

   Affiliation as printed

   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

7. Anthony J. Banday

   Centre National de la Recherche Scientifique · Université Toulouse III - Paul Sabatier · Institut de Recherche en Astrophysique et Planétologie · Université de Toulouse

   Affiliation as printed

   CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse cedex 4, France

   Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France

8. R. Belén Barreiro

   Universidad de Cantabria · Instituto de Física de Cantabria

   Affiliation as printed

   Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain

9. N. Bartolo

   University of Padua · Istituto Nazionale di Fisica Nucleare, Sezione di Padova

   Affiliation as printed

   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

10. S. Basak

    Indian Institute of Science Education and Research Thiruvananthapuram

    Affiliation as printed

    School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Maruthamala PO, Vithura, Thiruvananthapuram, 695551 Kerala, India

11. K. Benabed

    Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université

    Affiliation as printed

    Institut d’Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

    Institut d'Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

12. J.-P. Bernard

    Centre National de la Recherche Scientifique · Université Toulouse III - Paul Sabatier · Institut de Recherche en Astrophysique et Planétologie · Université de Toulouse

    Affiliation as printed

    CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse cedex 4, France

    Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France

13. Marco Bersanelli

    University of Milan · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy

    INAF/IASF Milano, Via E. Bassini 15, Milano, Italy

14. P. Bielewicz

    Scuola Internazionale Superiore di Studi Avanzati · National Centre for Nuclear Research

    Affiliation as printed

    National Centre for Nuclear Research, ul. L. Pasteura 7, 02-093 Warsaw, Poland

    SISSA, Astrophysics Sector, Via Bonomea 265, 34136 Trieste, Italy

15. J. Richard Bond

    University of Toronto · Canadian Institute for Theoretical Astrophysics

    Affiliation as printed

    CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada

16. Jullian Borrill

    Lawrence Berkeley National Laboratory · Space Sciences Laboratory · University of California, Berkeley

    Affiliation as printed

    Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Space Sciences Laboratory, University of California, Berkeley, CA, USA

17. François R. Bouchet

    Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université

    Affiliation as printed

    Institut d’Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

    Institut d'Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

18. M. Bucher

    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

    Affiliation as printed

    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

    Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa

19. C. Burigana

    University of Ferrara · Istituto di Radioastronomia di Bologna · Istituto Nazionale di Fisica Nucleare, Sezione di Bologna

    Affiliation as printed

    Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy

    INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy

    INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy

20. R. C. Butler

    Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    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

21. E. Calabrese

    Cardiff University

    Affiliation as printed

    School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, UK

22. J.-F. Cardoso

    Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université

    Affiliation as printed

    Institut d’Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

    Institut d'Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

23. B. Casaponsa

    Universidad de Cantabria · Instituto de Física de Cantabria

    Affiliation as printed

    Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain

24. A. Challinor

    University of Cambridge

    Affiliation as printed

    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

25. H. C. Chiang

    Princeton University · University of KwaZulu-Natal

    Affiliation as printed

    Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa

    Department of Physics, Princeton University, Princeton, NJ, USA

26. L. P. L. Colombo

    University of Milan

    Affiliation as printed

    Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy

27. Céline Combet

    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

    Affiliation as printed

    Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France

28. Brendan P. Crill

    California Institute of Technology · Jet Propulsion Laboratory

    Affiliation as printed

    California Institute of Technology, Pasadena, CA, USA

    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA

29. F. Cuttaia

    Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    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

30. P. de Bernardis

    Sapienza University of Rome

    Affiliation as printed

    Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, Roma, Italy

31. A. de Rosa

    Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    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

32. G. de Zotti

    Osservatorio Astronomico di Padova · National Institute for Astrophysics

    Affiliation as printed

    INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, Italy

    INAF – Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, Padova, Italy

33. J.‐M. Delouis

    Centre National de la Recherche Scientifique · Ifremer · Laboratory for Ocean Physics and Satellite Remote Sensing · Institut de Recherche pour le Développement

    Affiliation as printed

    Laboratoire d’Océanographie Physique et Spatiale (LOPS), Univ. Brest, CNRS, Ifremer, IRD, Brest, France

    Laboratoire d'Océanographie Physique et Spatiale (LOPS), Univ. Brest, CNRS, Ifremer, IRD, Brest, France

34. Eleonora Di Valentino

    University of Manchester

    Affiliation as printed

    Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK

35. Jose Maria Diego

    Universidad de Cantabria · Instituto de Física de Cantabria

    Affiliation as printed

    Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain

36. Olivier Doré

    California Institute of Technology · Jet Propulsion Laboratory

    Affiliation as printed

    California Institute of Technology, Pasadena, CA, USA

    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA

37. Marian Douspis

    Université Paris-Sud · Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut d'Astrophysique Spatiale

    Affiliation as printed

    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

38. Anne Ducout

    Kavli Institute for the Physics and Mathematics of the Universe · The University of Tokyo

    Affiliation as printed

    Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), UTIAS, The University of Tokyo, Chiba 277- 8583, Japan

39. X. Dupac

    European Space Agency · European Space Astronomy Centre

    Affiliation as printed

    European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain

40. S. Dusini

    Istituto Nazionale di Fisica Nucleare, Sezione di Padova

    Affiliation as printed

    Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy

41. G. Efstathiou

    University of Cambridge

    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

42. F. Elsner

    Max Planck Institute for Astrophysics

    Affiliation as printed

    Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany

43. Torsten A. Enßlin

    Max Planck Institute for Astrophysics

    Affiliation as printed

    Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany

44. Hans Kristian Eriksen

    University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway

45. Yabebal T. Fantaye

    African Institute for Mathematical Sciences · Stellenbosch University

    Affiliation as printed

    African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg, Cape Town, South Africa

    Department of Mathematics, University of Stellenbosch, Stellenbosch 7602, South Africa

46. J. Fergusson

    University of Cambridge

    Affiliation as printed

    Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

47. R. Fernández-Cobos

    Universidad de Cantabria · Instituto de Física de Cantabria

    Affiliation as printed

    Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain

48. Fabio Finelli

    Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    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

    INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy

49. M. Frailis

    Trieste Astronomical Observatory

    Affiliation as printed

    INAF – Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, Italy

50. A. A. Fraisse

    Princeton University

    Affiliation as printed

    Department of Physics, Princeton University, Princeton, NJ, USA

51. Enrico Franceschi

    Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    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

52. Samuele Galeotta

    Trieste Astronomical Observatory

    Affiliation as printed

    INAF – Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, Italy

53. S. Galli

    Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université

    Affiliation as printed

    Institut d’Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

    Institut d'Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

54. Ken M. Ganga

    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

    Affiliation as printed

    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

55. R. T. Génova-Santos

    Universidad de La Laguna · Instituto de Astrofísica de Canarias

    Affiliation as printed

    Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain

    Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, Tenerife, Spain

56. M. Gerbino

    Argonne National Laboratory

    Affiliation as printed

    HEP Division, Argonne National Laboratory, Lemont, IL 60439, USA

57. J. González-Nuevo

    Universidad de Oviedo

    Affiliation as printed

    Departamento de Física, Universidad de Oviedo, C/ Federico García Lorca, 18, Oviedo, Spain

58. Krzysztof M. Gorski

    California Institute of Technology · Jet Propulsion Laboratory · University of Warsaw

    Affiliation as printed

    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA

    Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

59. S. Gratton

    University of Cambridge

    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

60. ALESSANDRO GRUPPUSO

    Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    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

    INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy

61. J. E. Gudmundsson

    Stockholm University · Princeton University · AlbaNova

    Affiliation as printed

    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

62. J. Hamann

    UNSW Sydney

    Affiliation as printed

    School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia

63. Will J. Handley

    University of Cambridge

    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

64. Frode K. Hansen

    University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway

65. D. Herranz

    Universidad de Cantabria · Instituto de Física de Cantabria

    Affiliation as printed

    Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain

66. Eric F. Hivon

    Centre National de la Recherche Scientifique · Institut d'Astrophysique de Paris · Sorbonne Université

    Affiliation as printed

    Institut d’Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

    Institut d'Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France

    Sorbonne Université, UMR7095, Institut d'Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

67. Zhiqi Huang

    Sun Yat-sen University

    Affiliation as printed

    School of Physics and Astronomy, Sun Yat-sen University, 2 Daxue Rd, Tangjia, Zhuhai, PR China

68. Andrew H. Jaffe

    Imperial College London

    Affiliation as printed

    Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK

69. William C. Jones

    Princeton University

    Affiliation as printed

    Department of Physics, Princeton University, Princeton, NJ, USA

70. Gabriel Jung

    University of Padua

    Affiliation as printed

    Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, Via Marzolo 8, 35131 Padova, Italy

71. Elina Keihänen

    University of Helsinki

    Affiliation as printed

    Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland

72. Reijo Keskitalo

    Lawrence Berkeley National Laboratory

    Affiliation as printed

    Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

73. K. Kiiveri

    University of Helsinki · Helsinki Institute of Physics

    Affiliation as printed

    Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland

    Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland

74. J. Kim

    Max Planck Institute for Astrophysics

    Affiliation as printed

    Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany

75. N. Krachmalnicoff

    Scuola Internazionale Superiore di Studi Avanzati

    Affiliation as printed

    SISSA, Astrophysics Sector, Via Bonomea 265, 34136 Trieste, Italy

76. Martin Kunz

    Université Paris-Sud · University of Geneva · Centre National de la Recherche Scientifique · African Institute for Mathematical Sciences · Université Paris-Saclay · Institut d'Astrophysique Spatiale

    Affiliation as printed

    African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg, Cape Town, South Africa

    Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Genève 4, Switzerland

    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

77. Hannu Kurki-Suonio

    University of Helsinki · Helsinki Institute of Physics

    Affiliation as printed

    Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland

    Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland

78. J.‐M. Lamarre

    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

    Affiliation as printed

    Sorbonne Université, Observatoire de Paris, Université PSL, École normale supérieure, CNRS, LERMA, 75005 Paris, France

79. Anthony Norden Lasenby

    University of Cambridge

    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

80. Massimiliano Lattanzi

    University of Ferrara · Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara

    Affiliation as printed

    Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy

    INFN, Sezione di Ferrara, Via Saragat 1, 44122 Ferrara, Italy

81. C. R. Lawrence

    California Institute of Technology · Jet Propulsion Laboratory

    Affiliation as printed

    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA

82. M. Le Jeune

    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

    Affiliation as printed

    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

83. F. Levrier

    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

    Affiliation as printed

    Sorbonne Université, Observatoire de Paris, Université PSL, École normale supérieure, CNRS, LERMA, 75005 Paris, France

84. Antony Lewis

    University of Sussex

    Affiliation as printed

    Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK

85. M. Liguori

    University of Padua · Istituto Nazionale di Fisica Nucleare, Sezione di Padova

    Affiliation as printed

    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

86. Per Barth Lilje

    University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway

87. V. Lindholm

    University of Helsinki · Helsinki Institute of Physics

    Affiliation as printed

    Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland

    Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland

88. M. López-Caniego

    European Space Agency · European Space Astronomy Centre

    Affiliation as printed

    European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain

89. Yin-Zhe Ma

    Purple Mountain Observatory · University of KwaZulu-Natal

    Affiliation as printed

    NAOC-UKZN Computational Astrophysics Centre (NUCAC), University of KwaZulu-Natal, Durban 4000, South Africa

    Purple Mountain Observatory, No. 8 Yuan Hua Road, 210034 Nanjing, PR China

    School of Chemistry and Physics, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa

90. Juan Francisco Macias-Perez

    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

    Affiliation as printed

    Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France

91. G. Maggio

    Trieste Astronomical Observatory

    Affiliation as printed

    INAF – Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, Italy

92. Davide Maino

    University of Milan · Istituto Nazionale di Fisica Nucleare, Sezione di Milano · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy

    INAF/IASF Milano, Via E. Bassini 15, Milano, Italy

    INFN, Sezione di Milano, Via Celoria 16, Milano, Italy

93. N. Mandolesi

    University of Ferrara · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy

    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

94. Airam Marcos-Caballero

    Universidad de Cantabria · Instituto de Física de Cantabria

    Affiliation as printed

    Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain

95. MICHELE MARIS

    Trieste Astronomical Observatory

    Affiliation as printed

    INAF – Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, Italy

96. Peter G. Martin

    University of Toronto · Canadian Institute for Theoretical Astrophysics

    Affiliation as printed

    CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada

97. Enrique Martínez-González

    Universidad de Cantabria · Instituto de Física de Cantabria

    Affiliation as printed

    Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain

98. S. Matarrese

    University of Padua · Istituto Nazionale di Fisica Nucleare, Sezione di Padova · Gran Sasso Science Institute

    Affiliation as printed

    Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, Via Marzolo 8, 35131 Padova, Italy

    Gran Sasso Science Institute, INFN, viale F. Crispi 7, 67100 L’Aquila, Italy

    Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy

    Gran Sasso Science Institute, INFN, viale F. Crispi 7, 67100 L'Aquila, Italy