Planck 2015 results

XX. Constraints on inflation

¹ 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
² Aalto University Metsähovi Radio Observatory and Dept of Radio Science and Engineering, PO Box 13000, 00076 Aalto, Finland
³ African Institute for Mathematical Sciences, 6−8 Melrose Road, Muizenberg, 7945 Cape Town, South Africa
⁴ Agenzia Spaziale Italiana Science Data Center, via del Politecnico snc, 00133 Roma, Italy
⁵ Aix-Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388 Marseille, France
⁶ Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB30 HE, UK
⁷ Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, 4000 Durban, South Africa
⁸ Atacama Large Millimeter/submillimeter Array, ALMA Santiago Central Offices, Alonso de Cordova 3107, Vitacura, 763 0355 Casilla, Santiago, Chile
⁹ CGEE, SCS Qd 9, Lote C, Torre C, 4° andar, Ed. Parque Cidade Corporate, CEP 70308-200 Brasília, DF, Brazil
¹⁰ CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
¹¹ CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
¹² CRANN, Trinity College, Dublin 2, Ireland
¹³ California Institute of Technology, Pasadena, CA 91125, USA
¹⁴ Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹⁵ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
¹⁶ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
¹⁷ Consejo Superior de Investigaciones Científicas (CSIC), 28049 Madrid, Spain
¹⁸ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁹ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
²⁰ Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Genève 4, Switzerland
²¹ Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen, Denmark
²² Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
²³ Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain
²⁴ Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, Ontario, ON M5S 3H41, Canada
²⁵ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²⁶ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²⁷ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles, CA 90089, USA
²⁸ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²⁹ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
³⁰ Department of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USA
³¹ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00560 Helsinki, Finland
³² Department of Physics, Princeton University, Princeton, NJ 08540, USA
³³ Department of Physics, University of California, Berkeley, CA 94720, USA
³⁴ Department of Physics, University of California, Santa Barbara, California, USA
³⁵ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
³⁶ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³⁷ Dipartimento di Fisica e Astronomia, ALMA MATER STUDIORUM, Università degli Studi di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
³⁸ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³⁹ Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00133 Roma, Italy
⁴⁰ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 00133 Milano, Italy
⁴¹ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 00133 Trieste, Italy
⁴² Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00133 Roma, Italy
⁴³ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 1165 Copenhagen, Denmark
⁴⁴ Discovery Center, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 1165 Copenhagen, Denmark
⁴⁵ European Southern Observatory, ESO Vitacura, Alonso de Cordova 3107, Vitacura, Casilla 19001, Santiago, Chile
⁴⁶ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, 28691 Villanueva de la Cañada, Madrid, Spain
⁴⁷ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴⁸ Gran Sasso Science Institute, INFN, viale F. Crispi 7, 67100 L’ Aquila, Italy
⁴⁹ HGSFP and University of Heidelberg, Theoretical Physics Department, Philosophenweg 16, 69120 Heidelberg, Germany
⁵⁰ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00560 Helsinki, Finland
⁵¹ INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35131 Padova, Italy
⁵² INAF–Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
⁵³ INAF–Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34127 Trieste, Italy
⁵⁴ INAF/IASF Bologna, via Gobetti 101, 40127 Bologna, Italy
⁵⁵ INAF/IASF Milano, via E. Bassini 15, 20133 Milano, Italy
⁵⁶ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁵⁷ INFN, Sezione di Roma 1, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy
⁵⁸ INFN, Sezione di Roma 2, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00185 Roma, Italy
⁵⁹ INFN/National Institute for Nuclear Physics, via Valerio 2, 34127 Trieste, Italy
⁶⁰ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Grenoble Alpes, IPAG, 38000 Grenoble, France; CNRS, IPAG, 38000 Grenoble, France
⁶¹ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁶² Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁶³ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁶⁴ Institut Néel, CNRS, Université Joseph Fourier Grenoble I, 25 rue des Martyrs, 38042 Grenoble, France
⁶⁵ Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁶⁶ Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay Cedex, France
⁶⁷ Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, France
⁶⁸ Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, 52056 Aachen, Germany
⁶⁹ Institute for Space Sciences, Bucharest-Magurale, Romania
⁷⁰ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁷¹ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0371 Oslo, Norway
⁷² Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, 28205 La Laguna, Tenerife, Spain
⁷³ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁷⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
⁷⁵ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁷⁶ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁷⁷ Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
⁷⁸ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁷⁹ Kazan Federal University, 18 Kremlyovskaya St., 420008 Kazan, Russia
⁸⁰ LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
⁸¹ LERMA, CNRS, Observatoire de Paris, 61 avenue de l’Observatoire, 75000 Paris, France
⁸² Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁸³ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault 75634 Paris Cedex 13, France
⁸⁴ Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁸⁵ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁸⁶ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁸⁷ Lebedev Physical Institute of the Russian Academy of Sciences, Astro Space Centre, 84/32 Profsoyuznaya st., 117997 Moscow, GSP-7, Russia
⁸⁸ Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, 10617 Taipei, Taiwan
⁸⁹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁹⁰ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁹¹ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁹² Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland
⁹³ Niels Bohr Institute, Blegdamsvej 17, 1165 Copenhagen, Denmark
⁹⁴ Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 1165 Copenhagen, Denmark
⁹⁵ Nordita (Nordic Institute for Theoretical Physics), Roslagstullsbacken 23, 106 91 Stockholm, Sweden
⁹⁶ Optical Science Laboratory, University College London, Gower Street, London, UK
⁹⁷ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁹⁸ SMARTEST Research Centre, Università degli Studi e-Campus, via Isimbardi 10, 22060 Novedrate (CO), Italy
⁹⁹ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
¹⁰⁰ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
¹⁰¹ Simon Fraser University, Department of Physics, 8888 University Drive, Burnaby BC, Canada
¹⁰² Sorbonne Université-UPMC, UMR 7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
¹⁰³ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, 117997 Moscow, Russia
¹⁰⁴ Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
¹⁰⁵ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
¹⁰⁶ Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USA
¹⁰⁷ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
¹⁰⁸ Sydney Institute for Astronomy, School of Physics A28, University of Sydney, NSW 2006, Australia
¹⁰⁹ The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics,Stockholm University, AlbaNova, 106 91 Stockholm, Sweden
¹¹⁰ Theory Division, PH-TH, CERN, 1211 Geneva 23, Switzerland
¹¹¹ UPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, France
¹¹² Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
¹¹³ Universities Space Research Association, Stratospheric Observatory for Infrared Astronomy, MS 232-11, Moffett Field, CA 94035, USA
¹¹⁴ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18071 Granada, Spain
¹¹⁵ University of Granada, Instituto Carlos I de Física Teórica y Computacional, 18071 Granada, Spain
¹¹⁶ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

^⋆ Corresponding author: Martin Bucher, e-mail: bucher@apc.univ-paris7.fr; Fabio Finelli, e-mail: finelli@iasfbo.inaf.it

Received: 14 February 2015
Accepted: 3 March 2016

Abstract

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be n_s = 0.968 ± 0.006 and tightly constrain its scale dependence to dn_s/ dlnk = −0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-ℓ polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r_0.002< 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r< 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) ∝ φ² and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R² inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth over the range of scales 0.008 Mpc^-1 ≲ k ≲ 0.1 Mpc^-1. At large scales, each method finds deviations from a power law, connected to a deficit at multipoles ℓ ≈ 20−40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is | α_{non - adi} | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum findingthat the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. These results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.