Planck 2015 results

XI. CMB power spectra, likelihoods, and robustness of parameters

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 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 CGEE, SCS Qd 9, Lote C, Torre C, 4° andar, Ed. Parque Cidade Corporate, CEP 70308-200, Brasília, DF, Brazil
⁹ CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
¹⁰ CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
¹¹ CRANN, Trinity College, Dublin, Ireland
¹² California Institute of Technology, Pasadena, California, USA
¹³ Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹⁴ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
¹⁵ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, California, USA
¹⁶ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁷ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
¹⁸ Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Genève 4, Switzerland
¹⁹ Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
²⁰ Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain
²¹ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²² Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²³ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles, CA 90089, USA
²⁴ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²⁵ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
²⁶ Department of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USA
²⁷ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00014 Helsinki, Finland
²⁸ Department of Physics, Princeton University, Princeton, NJ 08544, USA
²⁹ Department of Physics, University of California, One Shields Avenue, Davis, CA 95616, USA
³⁰ Department of Physics, University of California, Santa Barbara, CA 93106, USA
³¹ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
³² Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³³ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³⁴ Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
³⁵ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, Italy
³⁶ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
³⁷ Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1, 00133 Roma, Italy
³⁸ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
³⁹ Discovery Center, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁴⁰ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, 28691 Villanueva de la Cañada, Madrid, Spain
⁴¹ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴² Gran Sasso Science Institute, INFN, viale F. Crispi 7, 67100 L’ Aquila, Italy
⁴³ HGSFP and University of Heidelberg, Theoretical Physics Department, Philosophenweg 16, 69120 Heidelberg, Germany
⁴⁴ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, PA 19041, USA
⁴⁵ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁴⁶ INAF–Osservatorio Astrofisico di Catania, via S. Sofia 78, Catania, Italy
⁴⁷ INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁴⁸ INAF– Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
⁴⁹ INAF–Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 40127 Trieste, 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, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁵³ INFN, Sezione di Ferrara, via Saragat 1, 44122 Ferrara, Italy
⁵⁴ INFN, Sezione di Roma 1, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy
⁵⁵ INFN, Sezione di Roma 2, Università di Roma Tor Vergata, via della Ricerca Scientifica 1, 00185 Roma, Italy
⁵⁶ INFN/National Institute for Nuclear Physics, via Valerio 2, 34127 Trieste, Italy
⁵⁷ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Grenoble Alpes, IPAG; CNRS, IPAG, 38000 Grenoble, France
⁵⁸ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁵⁹ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁶⁰ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁶¹ Institut Néel, CNRS, Université Joseph Fourier Grenoble I, 25 rue des Martyrs, 38042 Grenoble, France
⁶² Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁶³ Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay Cedex, France
⁶⁴ Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, France
⁶⁵ Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, 52056 Aachen, Germany
⁶⁶ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶⁷ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0371 Oslo, Norway
⁶⁸ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, 38205 Tenerife, Spain
⁶⁹ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 93005 Santander, Spain
⁷⁰ Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
⁷¹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 31109, USA
⁷² Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁷³ Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
⁷⁴ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁷⁵ Kazan Federal University, 18 Kremlyovskaya St., 420008 Kazan, Russia
⁷⁶ LAL, Université Paris-Sud, CNRS/IN2P3, 91898 Orsay, France
⁷⁷ LERMA, CNRS, Observatoire de Paris, 61 avenue de l’Observatoire, 75014 Paris, France
⁷⁸ Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁷⁹ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault 75634 Paris Cedex 13, France
⁸⁰ Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁸¹ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁸² Lebedev Physical Institute of the Russian Academy of Sciences, Astro Space Centre, 84/32 Profsoyuznaya st., GSP-7, 117997 Moscow, Russia
⁸³ Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, 10617 Taipei, Taiwan
⁸⁴ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁸⁵ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁸⁶ Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland
⁸⁷ Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁸⁸ Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁸⁹ Nordita (Nordic Institute for Theoretical Physics), Roslagstullsbacken 23, 106 91 Stockholm, Sweden
⁹⁰ Optical Science Laboratory, University College London, Gower Street, London, UK
⁹¹ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁹² SMARTEST Research Centre, Università degli Studi e-Campus, Via Isimbardi 10, Novedrate (CO), 22060, Italy
⁹³ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁹⁴ Sorbonne Université-UPMC, UMR 7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
⁹⁵ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, 117997 Moscow, Russia
⁹⁶ Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
⁹⁷ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
⁹⁸ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
⁹⁹ Sydney Institute for Astronomy, School of Physics A28, University of Sydney, NSW 2006, Australia
¹⁰⁰ The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, 106 91 Stockholm, Sweden
¹⁰¹ Theory Division, PH-TH, CERN, 1211 Geneva 23, Switzerland
¹⁰² UPMC Univ. Paris 06, UMR 7095, 98bis boulevard Arago, 75014 Paris, France
¹⁰³ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
¹⁰⁴ University Observatory, Ludwig Maximilian University of Munich, Scheinerstrasse 1, 81679 Munich, Germany
¹⁰⁵ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18071 Granada, Spain
¹⁰⁶ University of Granada, Instituto Carlos I de Física Teórica y Computacional, 18071 Granada, Spain
¹⁰⁷ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

^⋆ Corresponding authors: F. R. Bouchet, e-mail: bouchet@iap.fr

Received: 9 July 2015
Accepted: 18 May 2016

Abstract

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlationfunctions of the cosmic microwave background (CMB) temperature and polarization fluctuations that account for relevant uncertainties, both instrumental and astrophysical in nature. They are based on the same hybrid approach used for the previous release, i.e., a pixel-based likelihood at low multipoles (ℓ< 30) and a Gaussian approximation to the distribution of cross-power spectra at higher multipoles. The main improvements are the use of more and better processed data and of Planck polarization information, along with more detailed models of foregrounds and instrumental uncertainties. The increased redundancy brought by more than doubling the amount of data analysed enables further consistency checks and enhanced immunity to systematic effects. It also improves the constraining power of Planck, in particular with regard to small-scale foreground properties. Progress in the modelling of foreground emission enables the retention of a larger fraction of the sky to determine the properties of the CMB, which also contributes to the enhanced precision of the spectra. Improvements in data processing and instrumental modelling further reduce uncertainties. Extensive tests establish the robustness and accuracy of the likelihood results, from temperature alone, from polarization alone, and from their combination. For temperature, we also perform a full likelihood analysis of realistic end-to-end simulations of the instrumental response to the sky, which were fed into the actual data processing pipeline; this does not reveal biases from residual low-level instrumental systematics. Even with the increase in precision and robustness, the ΛCDM cosmological model continues to offer a very good fit to the Planck data. The slope of the primordial scalar fluctuations, n_s, is confirmed smaller than unity at more than 5σ from Planck alone. We further validate the robustness of the likelihood results against specific extensions to the baseline cosmology, which are particularly sensitive to data at high multipoles. For instance, the effective number of neutrino species remains compatible with the canonical value of 3.046. For this first detailed analysis of Planck polarization spectra, we concentrate at high multipoles on the E modes, leaving the analysis of the weaker B modes to future work. At low multipoles we use temperature maps at all Planck frequencies along with a subset of polarization data. These data take advantage of Planck’s wide frequency coverage to improve the separation of CMB and foreground emission. Within the baseline ΛCDM cosmology this requires τ = 0.078 ± 0.019 for the reionization optical depth, which is significantly lower than estimates without the use of high-frequency data for explicit monitoring of dust emission. At high multipoles we detect residual systematic errors in E polarization, typically at the μK² level; we therefore choose to retain temperature information alone for high multipoles as the recommended baseline, in particular for testing non-minimal models. Nevertheless, the high-multipole polarization spectra from Planck are already good enough to enable a separate high-precision determination of the parameters of the ΛCDM model, showing consistency with those established independently from temperature information alone.