Planck 2013 results. XXIV. Constraints on primordial non-Gaussianity

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, Metsähovintie 114, 02540 Kylmälä, Finland
³ African Institute for Mathematical Sciences, 6-8 Melrose Road, 7945 Muizenberg, Cape Town, South Africa
⁴ Agenzia Spaziale Italiana Science Data Center, via del Politecnico snc, 00133 Roma, Italy
⁵ Agenzia Spaziale Italiana, viale Liegi 26, 00998 Roma, Italy
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, 4000 Durban, 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 California Institute of Technology, Pasadena, California, USA
¹¹ Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹² Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
¹³ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, California, USA
¹⁴ Consejo Superior de Investigaciones Científicas (CSIC), 2800 Madrid, Spain
¹⁵ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁶ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
¹⁷ Département de Physique Théorique, Université de Genève, 24 Quai E. Ansermet, 1211 Genève 4, Switzerland
¹⁸ Departamento de Física Fundamental, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain
¹⁹ Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain
²⁰ Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, Ontario, Canada
²¹ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²² Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA
²³ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²⁴ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles CA 90089, USA
²⁵ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²⁶ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
²⁷ Department of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USA
²⁸ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00014 Helsinki, Finland
²⁹ Department of Physics, Princeton University, Princeton, New Jersey, USA
³⁰ Department of Physics, University of California, Berkeley, California, USA
³¹ Department of Physics, University of California, One Shields Avenue, Davis, California, USA
³² Department of Physics, University of California, Santa Barbara, California, USA
³³ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
³⁴ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³⁵ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³⁶ Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
³⁷ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, Italy
³⁸ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
³⁹ Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1, 00133 Roma, Italy
⁴⁰ Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1, 00133 Roma, Italy
⁴¹ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁴² Dpto. Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
⁴³ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo s/n, Urbanización Villafranca del Castillo, 28691 Villanueva de la Cañada, Madrid, Spain
⁴⁴ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴⁵ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁴⁶ INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁴⁷ INAF – Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
⁴⁸ INAF – Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34143 Trieste, Italy
⁴⁹ INAF Istituto di Radioastronomia, via P. Gobetti 101, 40129 Bologna, Italy
⁵⁰ INAF/IASF Bologna, via Gobetti 101, 40129 Bologna, Italy
⁵¹ INAF/IASF Milano, via E. Bassini 15, 20133 Milano, Italy
⁵² INFN, Sezione di Bologna, via Irnerio 46, 40126, Bologna, Italy
⁵³ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁵⁴ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, France
⁵⁵ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁵⁶ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁵⁷ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena CA 91125, USA
⁵⁸ Institut Néel, CNRS, Université Joseph Fourier Grenoble I, 25 rue des Martyrs, 38042 Grenoble, France
⁵⁹ Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁶⁰ Institut d’Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, France
⁶¹ Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98bis Boulevard Arago, 75014 Paris, France
⁶² Institute for Space Sciences, 077125 Bucharest-Magurale, Romania
⁶³ Institute of Astronomy and Astrophysics, Academia Sinica, 106 Taipei, Taiwan
⁶⁴ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶⁵ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0315 Oslo, Norway
⁶⁶ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, 38200 La Laguna, Tenerife, Spain
⁶⁷ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁶⁸ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁶⁹ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁷⁰ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁷¹ LAL, Université Paris-Sud, CNRS/IN2P3, 91383 Orsay, France
⁷² LERMA, CNRS, Observatoire de Paris, 61 Avenue de l’Observatoire, 75014 Paris, France
⁷³ Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁷⁴ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁷⁵ Laboratoire de Physique Subatomique et de Cosmologie, Université Joseph Fourier Grenoble I, CNRS/IN2P3, Institut National Polytechnique de Grenoble, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁷⁶ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁷⁷ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁷⁸ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁷⁹ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁸⁰ MilliLab, VTT Technical Research Centre of Finland, Tietotie 3, 02044 Espoo, Finland
⁸¹ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁸² Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁸³ Observational Cosmology, Mail Stop 367-17, California Institute of Technology, Pasadena CA, 91125, USA
⁸⁴ Optical Science Laboratory, University College London, Gower Street, London, UK
⁸⁵ SB-ITP-LPPC, EPFL, 1015 Lausanne, Switzerland
⁸⁶ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁸⁷ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁸⁸ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁸⁹ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, 117997 Moscow, Russia
⁹⁰ Space Sciences Laboratory, University of California, Berkeley, California, USA
⁹¹ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167, Karachai-Cherkessian Republic, Russia
⁹² Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USA
⁹³ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
⁹⁴ Theory Division, PH-TH, CERN, 1211 Geneva 23, Switzerland
⁹⁵ UPMC Univ. Paris 06, UMR7095, 98bis Boulevard Arago, 75014 Paris, France
⁹⁶ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
⁹⁷ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18071 Granada, Spain
⁹⁸ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 22 March 2013
Accepted: 16 December 2013

Abstract

The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result f_NL^local = 2.7 ± 5.8, f_NL^equil = -42 ± 75, and f_NL^orth = -25 ± 39 (68% CL statistical). Non-Gaussianity is detected in the data; using skew-C_ℓ statistics we find a nonzero bispectrum from residual point sources, and the integrated-Sachs-Wolfe-lensing bispectrum at a level expected in the ΛCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-C_ℓ, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the Planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, including general single-field models of inflation, excited initial states (non-Bunch-Davies vacua), and directionally-dependent vector models. We provide an initial survey of scale-dependent feature and resonance models. These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, c_s ≥ 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction r_D ≥ 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the four-point function in the local model τ_NL< 2800 (95% CL). Taken together, these constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.