Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts

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 Academy of Sciences of Tatarstan, Bauman Str., 20, Kazan, 420111 Republic of Tatarstan, Russia
⁴ African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg, 7701 Rondebosch Cape Town, South Africa
⁵ Agenzia Spaziale Italiana Science Data Center, c/o ESRIN, via Galileo Galilei, 00044 Frascati, Italy
⁶ Agenzia Spaziale Italiana, Viale Liegi 26, 00198 Roma, Italy
⁷ Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
⁸ Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, 4000 Durban, South Africa
⁹ Atacama Large Millimeter/submillimeter Array, ALMA Santiago Central Offices, Alonso de Cordova 3107, Vitacura, Casilla 763 0355 Santiago, Chile
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 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 Astrofísica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
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, California, USA
¹⁷ Consejo Superior de Investigaciones Científicas (CSIC), 28006 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 Departamento de Física Fundamental, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain
²² Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain
²³ Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, Ontario, Canada
²⁴ Department of Astronomy and Geodesy, Kazan Federal University, Kremlevskaya Str., 18, 420008 Kazan, Russia
²⁵ Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
²⁶ Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA
²⁷ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²⁸ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles, CA 90089, USA
²⁹ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
³⁰ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
³¹ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00014 Helsinki, Finland
³² Department of Physics, Princeton University, Princeton, New Jersey, USA
³³ Department of Physics, University of California, Berkeley, California, USA
³⁴ Department of Physics, University of California, One Shields Avenue, Davis, California, USA
³⁵ Department of Physics, University of California, Santa Barbara, California, USA
³⁶ Department of Physics, University of Illinois at Urbana- Champaign, 1110 West Green Street, Urbana, Illinois, USA
³⁷ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, 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, 00185 Roma, Italy
⁴⁰ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, 20133 Milano, Italy
⁴¹ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
⁴² Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00133 Roma, Italy
⁴³ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁴⁴ Dpto. Astrofísica, Universidad de La Laguna (ULL), 38206, La Laguna, Tenerife, Spain
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 Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Väisäläntie 20, 21500 Piikkiö, Finland
⁴⁹ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, Pennsylvania, USA
⁵⁰ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁵¹ INAF – Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123 Catania, Italy
⁵² INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁵³ INAF – Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
⁵⁴ INAF – Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, Trieste, Italy
⁵⁵ INAF/IASF Bologna, via Gobetti 101, 40129 Bologna, Italy
⁵⁶ INAF/IASF Milano, via E. Bassini 15, 20133 Milano, Italy
⁵⁷ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁵⁸ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁵⁹ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, France
⁶⁰ ISDC Data Centre for Astrophysics, University of Geneva, Ch. d’Ecogia 16, 1290 Versoix, Switzerland
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 (UMR 8617) Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, France
⁶⁷ Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, France
⁶⁸ Institute for Space Sciences, 07745 Bucharest-Magurale, Romania
⁶⁹ Institute of Astronomy and Astrophysics, Academia Sinica, 10617 Taipei, Taiwan
⁷⁰ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁷¹ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0315 Oslo, Norway
⁷² Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, 38200, La Laguna, Tenerife, Spain
⁷³ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁷⁴ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁷⁵ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁷⁶ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁷⁷ LAL, Université Paris-Sud, CNRS/IN2P3, 91898 Orsay, France
⁷⁸ LERMA, CNRS, Observatoire de Paris, 61 avenue de l’Observatoire, 75014 Paris, France
⁷⁹ Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁸⁰ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁸¹ Laboratoire de PhysiqueSubatomique et de Cosmologie, Université Joseph Fourier Grenoble I, CNRS/IN2P3, Institut National Polytechnique de Grenoble, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁸² Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁸³ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁸⁴ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁸⁵ Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstraße, 85748 Garching, Germany
⁸⁶ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁸⁷ MilliLab, VTT Technical Research Centre of Finland, Tietotie 3, Espoo, Finland
⁸⁸ Moscow Institute of Physics and Technology, Institutsky per., 9, 141700 Dolgoprudny, Russia
⁸⁹ Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁹⁰ Observational Cosmology, Mail Stop 367-17, California Institute of Technology, Pasadena, CA, 91125, USA
⁹¹ Optical Science Laboratory, University College London, Gower Street, London, UK
⁹² SB-ITP-LPPC, EPFL, CH-1015 Lausanne, Switzerland
⁹³ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁹⁴ SUPA, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁹⁵ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁹⁶ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁹⁷ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, 117997 Moscow, Russia
⁹⁸ Space Sciences Laboratory, University of California, Berkeley, California, USA
⁹⁹ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
¹⁰⁰ Stanford University, Dept of Physics, Varian Physics Bldg, 382 Via Pueblo Mall, Stanford, California, USA
¹⁰¹ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
¹⁰² Tübitak National Observatory, Akdeniz University Campus, 07058 Antalya, Turkey
¹⁰³ Theory Division, PH-TH, CERN, 1211 Geneva 23, Switzerland
¹⁰⁴ UPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, France
¹⁰⁵ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
¹⁰⁶ University Observatory, Ludwig Maximilian University of Munich, Scheinerstrasse 1, 81679 Munich, Germany
¹⁰⁷ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18071 Granada, Spain
¹⁰⁸ University of Miami, Knight Physics Building, 1320 Campo Sano Dr., Coral Gables, Florida, USA
¹⁰⁹ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 20 March 2013
Accepted: 4 February 2014

Abstract

We present constraints on cosmological parameters using number counts as a function of redshift for a sub-sample of 189 galaxy clusters from the Planck SZ (PSZ) catalogue. The PSZ is selected through the signature of the Sunyaev-Zeldovich (SZ) effect, and the sub-sample used here has a signal-to-noise threshold of seven, with each object confirmed as a cluster and all but one with a redshift estimate. We discuss the completeness of the sample and our construction of a likelihood analysis. Using a relation between mass M and SZ signal Y calibrated to X-ray measurements, we derive constraints on the power spectrum amplitude σ₈ and matter density parameter Ω_m in a flat ΛCDM model. We test the robustness of our estimates and find that possible biases in the Y–M relation and the halo mass function are larger than the statistical uncertainties from the cluster sample. Assuming the X-ray determined mass to be biased low relative to the true mass by between zero and 30%, motivated by comparison of the observed mass scaling relations to those from a set of numerical simulations, we find that σ₈ = 0.75 ± 0.03, Ω_m = 0.29 ± 0.02, and σ₈(Ω_m/ 0.27)^0.3 = 0.764 ± 0.025. The value of σ₈ is degenerate with the mass bias; if the latter is fixed to a value of 20% (the central value from numerical simulations) we find σ₈(Ω_m/0.27)^0.3 = 0.78 ± 0.01 and a tighter one-dimensional range σ₈ = 0.77 ± 0.02. We find that the larger values of σ₈ and Ω_m preferred by Planck’s measurements of the primary CMB anisotropies can be accommodated by a mass bias of about 40%. Alternatively, consistency with the primary CMB constraints can be achieved by inclusion of processes that suppress power on small scales relative to the ΛCDM model, such as a component of massive neutrinos. We place our results in the context of other determinations of cosmologicalparameters, and discuss issues that need to be resolved in order to make further progress in this field.