Planck 2013 results. XXV. Searches for cosmic strings and other topological defects

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, Muizenberg, 7701 Rondebosch Cape Town, South Africa
⁴ Agenzia Spaziale Italiana Science Data Center, c/o ESRIN, via Galileo Galilei, 00044 Frascati, 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 & 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), 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 andSciences, 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, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland
²⁷ Department of Physics, Princeton University, Princeton, New Jersey, USA
²⁸ Department of Physics, University of California, One Shields Avenue, Davis, California, USA
²⁹ Department of Physics, University of California, Santa Barbara, California, USA
³⁰ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
³¹ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³² Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³³ Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
³⁴ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, Italy
³⁵ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
³⁶ Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1, 00133 Roma, Italy
³⁷ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
³⁸ Dpto. Astrofísica, Universidad de La Laguna (ULL), 38206, La Laguna, Tenerife, Spain
³⁹ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo s/n, Urbanización Villafranca del Castillo, 28691 Villanueva de la Cañada, Madrid, Spain
⁴⁰ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴¹ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁴² INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁴³ INAF – Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
⁴⁴ INAF – Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34131 Trieste, Italy
⁴⁵ INAF/IASF Bologna, via Gobetti 101, 40129 Bologna, Italy
⁴⁶ INAF/IASF Milano, via E. Bassini 15, 20133 Milano, Italy
⁴⁷ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁴⁸ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁴⁹ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, France
⁵⁰ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁵¹ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁵² Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁵³ Institut Néel, CNRS, Université Joseph Fourier Grenoble I, 25 rue des Martyrs, 38042 Grenoble, France
⁵⁴ Institut Universitaire de France, 103 Bd Saint-Michel, 75005 Paris, France
⁵⁵ Institut d’Astrophysique Spatiale, CNRS (UMR8617) Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, France
⁵⁶ Institut d’Astrophysique de Paris, CNRS (UMR7095), 98bis Bd Arago, 75014 Paris, France
⁵⁷ Institute for Space Sciences, 077125 Bucharest-Magurale, Romania
⁵⁸ Institute of Astronomy and Astrophysics, Academia Sinica, 10617 Taipei, Taiwan
⁵⁹ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶⁰ Institute of Mathematics and Physics, Centre for Cosmology, Particle Physics and Phenomenology, 1348 Louvain University, Louvain-la-Neuve, Belgium
⁶¹ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0315 Oslo, Norway
⁶² Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, 38200 La Laguna, Tenerife, Spain
⁶³ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁶⁴ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁶⁵ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁶⁶ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁶⁷ LAL, Université Paris-Sud, CNRS/IN2P3, 91898 Orsay, France
⁶⁸ LERMA, CNRS, Observatoire de Paris, 61 Avenue de l’Observatoire, 75014 Paris, France
⁶⁹ Laboratoire AIM,IRFU/Service d’Astrophysique - CEA/DSM - CNRS - Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁷⁰ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁷¹ 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
⁷² Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁷³ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁷⁴ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁷⁵ Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstraße, 85748 Garching, Germany
⁷⁶ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁷⁷ MilliLab, VTT Technical Research Centre of Finland, Tietotie 3, 02044 Espoo, Finland
⁷⁸ Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁷⁹ Observational Cosmology, Mail Stop 367-17, California Institute of Technology, Pasadena, CA, 91125, USA
⁸⁰ Optical Science Laboratory, University College London, Gower Street, London, UK
⁸¹ SB-ITP-LPPC, EPFL, 1015, Lausanne, Switzerland
⁸² SISSA, Astrophysics Sector, via Bonomea 265, 34136, Trieste, Italy
⁸³ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁸⁴ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁸⁵ Space Sciences Laboratory, University of California, Berkeley, California, USA
⁸⁶ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
⁸⁷ Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USA
⁸⁸ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
⁸⁹ Theory Division, PH-TH, CERN, 1211 Geneva 23, Switzerland
⁹⁰ UPMC Univ. Paris 06, UMR7095, 98bis Boulevard Arago, 75014 Paris, France
⁹¹ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
⁹² University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 1807 Granada, Spain
⁹³ University of Miami, Knight Physics Building, 1320 Campo Sano Dr., Coral Gables, Florida, USA
⁹⁴ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 1 April 2013
Accepted: 23 January 2014

Abstract

Planck data have been used to provide stringent new constraints on cosmic strings and other defects. We describe forecasts of the CMB power spectrum induced by cosmic strings, calculating these from network models and simulations using line-of-sight Boltzmann solvers. We have studied Nambu-Goto cosmic strings, as well as field theory strings for which radiative effects are important, thus spanning the range of theoretical uncertainty in the underlying strings models. We have added the angular power spectrum from strings to that for a simple adiabatic model, with the extra fraction defined as f₁₀ at multipole ℓ = 10. This parameter has been added to the standard six parameter fit using COSMOMC with flat priors. For the Nambu-Goto string model, we have obtained a constraint on the string tension of Gμ/c² < 1.5 × 10^-7 and f₁₀ < 0.015 at 95% confidence that can be improved to Gμ/c² < 1.3 × 10^-7 and f₁₀ < 0.010 on inclusion of high-ℓ CMB data. For the Abelian-Higgs field theory model we find, Gμ_AH/c²< 3.2 × 10^-7 and f₁₀ < 0.028. The marginalised likelihoods for f₁₀ and in the f₁₀–Ω_bh² plane are also presented. We have additionally obtained comparable constraints on f₁₀ for models with semilocal strings and global textures. In terms of the effective defect energy scale these are somewhat weaker at Gμ/c² < 1.1 × 10^-6. We have made complementarity searches for the specific non-Gaussian signatures of cosmic strings, calibrating with all-sky Planck resolution CMB maps generated from networks of post-recombination strings. We have validated our non-Gaussian searches using these simulated maps in a Planck-realistic context, estimating sensitivities of up to ΔGμ/c² ≈ 4 × 10^-7. We have obtained upper limits on the string tension at 95% confidence of Gμ/c² < 9.0 × 10^-7 with modal bispectrum estimation and Gμ/c² < 7.8 × 10^-7 for real space searches with Minkowski functionals. These are conservative upper bounds because only post-recombination string contributions have been included in the non-Gaussian analysis.