Planck 2018 results

X. Constraints on inflation

¹ AIM, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
² AIM, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
³ 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
⁴ African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg, Cape Town, South Africa
⁵ Aix Marseille Univ., CNRS, CNES, LAM, Marseille, France
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, Durban 4000, South Africa
⁸ CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
⁹ CNRS, IRAP, 9 Av. Colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
¹⁰ Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
¹¹ California Institute of Technology, Pasadena, CA, USA
¹² Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹³ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
¹⁴ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
¹⁵ Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Genève 4, Switzerland
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 Nijmegen, The Netherlands
¹⁹ Department of General Education, National Institute of Technology, Kagawa College, 355 Chokushi-cho, Takamatsu, Kagawa 761-8058, Japan
²⁰ Department of Mathematics, University of Stellenbosch, Stellenbosch 7602, South Africa
²¹ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC, Canada
²² Department of Physics & Astronomy, University of the Western Cape, Cape Town 7535, South Africa
²³ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²⁴ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
²⁵ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland
²⁶ Department of Physics, Princeton University, Princeton, NJ, USA
²⁷ Department of Physics, University of California, Santa Barbara, CA, USA
²⁸ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL, 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 Noordwijk, The Netherlands
³⁷ Gran Sasso Science Institute, INFN, Viale F. Crispi 7, 67100 L’Aquila, Italy
³⁸ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, PA, USA
³⁹ Helsinki Institute of Physics, University of Helsinki, Gustaf Hällströmin katu 2, Helsinki, Finland
⁴⁰ 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
⁴¹ INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, Italy
⁴² INAF – Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, Italy
⁴³ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
⁴⁴ INAF/IASF Milano, Via E. Bassini 15, Milano, Italy
⁴⁵ INFN – CNAF, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁶ INFN, Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁷ INFN, Sezione di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
⁴⁸ INFN, Sezione di Milano, Via Celoria 16, Milano, Italy
⁴⁹ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁵⁰ INFN, Sezione di Roma 2, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, Roma, Italy
⁵¹ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, Pune 411 007, India
⁵² Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK
⁵³ Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay Cedex, France
⁵⁴ Institut d’Astrophysique de Paris, CNRS (UMR7095), 98bis boulevard Arago, 75014 Paris, France
⁵⁵ Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, 52056 Aachen, Germany
⁵⁶ Institute Lorentz, Leiden University, PO Box 9506, Leiden 2300, 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 Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
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 Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
⁶⁶ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶⁷ LERMA, CNRS, Observatoire de Paris, 61 avenue de l’Observatoire, Paris, France
⁶⁸ LERMA/LRA, Observatoire de Paris, PSL Research University, CNRS, Ecole Normale Supérieure, 75005 Paris, France
⁶⁹ Laboratoire AIM, CEA – Université Paris-Saclay, 91191 Gif-sur-Yvette, France
⁷⁰ Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁷¹ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁷² Lawrence Berkeley National Laboratory, Berkeley, CA, USA
⁷³ Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan
⁷⁴ Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo 00076, Aalto, Finland
⁷⁵ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁷⁶ Mullard Space Science Laboratory, University College London, Surrey RH5 6NT, UK
⁷⁷ NAOC-UKZN Computational Astrophysics Centre (NUCAC), University of KwaZulu-Natal, Durban 4000, South Africa
⁷⁸ Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warsaw, Poland
⁷⁹ SISSA, Astrophysics Sector, Via Bonomea 265, 34136 Trieste, Italy
⁸⁰ San Diego Supercomputer Center, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
⁸¹ School of Chemistry and Physics, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa
⁸² School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni, 752050, Odissa, India
⁸³ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, UK
⁸⁴ School of Physics and Astronomy, Sun Yat-sen University, 2 Daxue Rd, Tangjia, Zhuhai, PR China
⁸⁵ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁸⁶ School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Maruthamala PO, Vithura, Thiruvananthapuram 695551, Kerala, India
⁸⁷ School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia
⁸⁸ Simon Fraser University, Department of Physics, 8888 University Drive, Burnaby, BC, Canada
⁸⁹ Sorbonne Université-UPMC, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
⁹⁰ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, Moscow 117997, Russia
⁹¹ Space Science Data Center – Agenzia Spaziale Italiana, Via del Politecnico snc, 00133 Roma, Italy
⁹² Space Sciences Laboratory, University of California, Berkeley, CA, USA
⁹³ The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova 106 91, Stockholm, Sweden
⁹⁴ UPMC Univ. Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, France
⁹⁵ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
⁹⁶ Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 Groningen, The Netherlands
⁹⁷ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 17 July 2018
Accepted: 19 August 2019

Abstract

We report on the implications for cosmic inflation of the 2018 release of the Planck cosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be n_s = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence of n_s, either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combining Planck with a compilation of baryon acoustic oscillation data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, r_0.002 <  0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r_0.002 <  0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential, V″(ϕ) < 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005 Mpc⁻¹ ≲ k ≲ 0.2 Mpc⁻¹. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectra. For the case of oscillatory features that are logarithmic or linear in k, this result is further strengthened by a new combined analysis including the Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively. Planck power spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.