Planck 2013 results. XXIII. Isotropy and statistics of the CMB

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, 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, 00198 Roma, Italy
⁶ Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
⁷ Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and 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), 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 Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain
²¹ Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, Ontario, Canada
²² Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²³ Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA
²⁴ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²⁵ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles, CA 90089, USA
²⁶ Department of Physics and Astronomy, University College London, London WC1E 6BT, 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 Alberta, 11322-89 Avenue, Edmonton, Alberta, T6G 2G7, Canada
³¹ Department of Physics, University of California, Berkeley, California, USA
³² Department of Physics, University of California, One Shields Avenue, Davis, California, USA
³³ Department of Physics, University of California, Santa Barbara, California, USA
³⁴ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
³⁵ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³⁶ Dipartimento di Fisica e Astronomia, Università degli Studi di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
³⁷ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³⁸ Dipartimento di Fisica, Università La Sapienza, P. le A. Moro 2, 00185 Roma, Italy
³⁹ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, Italy
⁴⁰ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
⁴¹ Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, Roma, 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, 2100 Copenhagen, Denmark
⁴⁴ Dpto. Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
⁴⁵ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain
⁴⁶ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴⁷ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁴⁸ INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, Italy
⁴⁹ INAF – Osservatorio Astronomico di Roma, via di Frascati 33, Monte Porzio Catone, Italy
⁵⁰ INAF – Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, Trieste, Italy
⁵¹ INAF Istituto di Radioastronomia, via P. Gobetti 101, 40129 Bologna, Italy
⁵² INAF/IASF Bologna, via Gobetti 101, 40129 Bologna, Italy
⁵³ INAF/IASF Milano, via E. Bassini 15, 20133 Milano, Italy
⁵⁴ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁵⁵ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁵⁶ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, France
⁵⁷ ISDC Data Centre for Astrophysics, University of Geneva, Ch. d’Ecogia 16, 1290 Versoix, Switzerland
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, 38054 Grenoble, France
⁶² Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁶³ Institut d’Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, France
⁶⁴ Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, France
⁶⁵ Institute for Space Sciences, 077125 Bucharest-Magurale, Romania
⁶⁶ Institute of Astronomy and Astrophysics, Academia Sinica, 106 Taipei, Taiwan
⁶⁷ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶⁸ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0315 Oslo, Norway
⁶⁹ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, 38200 Tenerife, Spain
⁷⁰ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁷¹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, 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 Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁷⁴ LAL, Université Paris-Sud, CNRS/IN2P3, 91898 Orsay, France
⁷⁵ LERMA, CNRS, Observatoire de Paris, 61 avenue de l’Observatoire, 75014 Paris, France
⁷⁶ Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁷⁷ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁷⁸ 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
⁷⁹ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁸⁰ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁸¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁸² Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstraße, 85748 Garching, Germany
⁸³ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁸⁴ MilliLab, VTT Technical Research Centre of Finland, Tietotie 3, Espoo, Finland
⁸⁵ Mullard Space Science Laboratory, University College London, Surrey RH5 6NT, UK
⁸⁶ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁸⁷ Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark
⁸⁸ Observational Cosmology, Mail Stop 367-17, California Institute of Technology, Pasadena, CA 91125, USA
⁸⁹ Optical Science Laboratory, University College London, Gower Street, London, UK
⁹⁰ SB-ITP-LPPC, EPFL, 1015, Lausanne, Switzerland
⁹¹ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁹² School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁹³ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁹⁴ Space Sciences Laboratory, University of California, Berkeley, California, USA
⁹⁵ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
⁹⁶ Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USA
⁹⁷ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
⁹⁸ Theory Division, PH-TH, CERN, 1211, Geneva 23, Switzerland
⁹⁹ UPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, France
¹⁰⁰ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
¹⁰¹ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, Granada, Spain
¹⁰² Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 21 March 2013
Accepted: 11 January 2014

Abstract

The two fundamental assumptions of the standard cosmological model – that the initial fluctuations are statistically isotropic and Gaussian – are rigorously tested using maps of the cosmic microwave background (CMB) anisotropy from the Planck satellite. The detailed results are based on studies of four independent estimates of the CMB that are compared to simulations using a fiducial ΛCDM model and incorporating essential aspects of the Planck measurement process. Deviations from isotropy have been found and demonstrated to be robust against component separation algorithm, mask choice, and frequency dependence. Many of these anomalies were previously observed in the WMAP data, and are now confirmed at similar levels of significance (about 3σ). However, we find little evidence of non-Gaussianity, with the exception of a few statistical signatures that seem to be associated with specific anomalies. In particular, we find that the quadrupole-octopole alignment is also connected to a low observed variance in the CMB signal. A power asymmetry is now found to persist on scales corresponding to about ℓ = 600 and can be described in the low-ℓ regime by a phenomenological dipole modulation model. However, any primordial power asymmetry is strongly scale-dependent and does not extend toarbitrarily small angular scales. Finally, it is plausible that some of these features may be reflected in the angular power spectrum of the data, which shows a deficit of power on similar scales. Indeed, when the power spectra of two hemispheres defined by a preferred direction are considered separately, one shows evidence of a deficit in power, while its opposite contains oscillations between odd and even modes that may be related to the parity violation and phase correlations also detected in the data. Although these analyses represent a step forward in building an understanding of the anomalies, a satisfactory explanation based on physically motivated models is still lacking.