Planck intermediate results

XXIV. Constraints on variations in fundamental constants^⋆

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 African Institute for Mathematical Sciences, 6−8 Melrose Road, Muizenberg, 7950 Cape Town, South Africa
³ Agenzia Spaziale Italiana Science Data Center, via del Politecnico snc, 00133 Roma, Italy
⁴ Agenzia Spaziale Italiana, viale Liegi 26, 00198 Roma, Italy
⁵ Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
⁶ Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, 4000 Durban, South Africa
⁷ Atacama Large Millimeter/submillimeter Array, ALMA Santiago Central Offices, Alonso de Cordova 3107, Vitacura, Casilla 763 0355, Santiago, Chile
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, CA 91125, USA
e-mail: graca@caltech.edu
¹¹ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
¹² Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
¹³ Consejo Superior de Investigaciones Científicas (CSIC), 28049 Madrid, Spain
¹⁴ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁵ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs, Lyngby, Denmark
¹⁶ Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Genève 4, Switzerland
¹⁷ Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain
¹⁸ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
¹⁹ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²⁰ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles, CA 90089, USA
²¹ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²² Department of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, FL, USA
²³ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland
²⁴ Department of Physics, Princeton University, Princeton, NJ, USA
²⁵ Department of Physics, University of California, Santa Barbara, CA, USA
²⁶ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
²⁷ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
²⁸ Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, Roma, Italy
²⁹ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16 Milano, Italy
³⁰ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, Trieste, Italy
³¹ Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1 Roma, Italy
³² Discovery Center, Niels Bohr Institute, Blegdamsvej 17 Copenhagen, Denmark
³³ Dpto. Astrofísica, Universidad de La Laguna (ULL), 38206, La Laguna, Tenerife, Spain
³⁴ European Southern Observatory, ESO Vitacura, Alonso de Cordova 3107, Vitacura, Casilla 19001, Santiago, Chile
³⁵ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain
³⁶ European Space Agency, ESTEC, Keplerlaan 1, 2201 Noordwijk, The Netherlands
³⁷ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
³⁸ INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, Italy
³⁹ INAF–Osservatorio Astronomico di Roma, via di Frascati 33, Monte Porzio Catone, Italy
⁴⁰ INAF–Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, Trieste, Italy
⁴¹ INAF/IASF Bologna, via Gobetti 101, Bologna, Italy
⁴² INAF/IASF Milano, via E. Bassini 15, Milano, Italy
⁴³ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁴⁴ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁴⁵ INFN/National Institute for Nuclear Physics, via Valerio 2, 34127 Trieste, Italy
⁴⁶ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, France
⁴⁷ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁴⁸ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁴⁹ Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁵⁰ Institut d’Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, Orsay, France
⁵¹ Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, France
⁵² Institute for Space Sciences, Bucharest-Magurale, Romania
⁵³ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁵⁴ Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
⁵⁵ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, Tenerife, Spain
⁵⁶ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
⁵⁷ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
⁵⁸ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁵⁹ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁶⁰ LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
⁶¹ LERMA, CNRS, Observatoire de Paris, 61 avenue de l’Observatoire, Paris, France
⁶² Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁶³ Laboratoire Univers et Théories (LUTh), UMR 8102 CNRS, Observatoire de Paris, Université Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France
⁶⁴ 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
⁶⁵ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁶⁶ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁶⁷ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁶⁸ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁶⁹ Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark
⁷⁰ Optical Science Laboratory, University College London, Gower Street, London, UK
⁷¹ SB-ITP-LPPC, EPFL, 1015 Lausanne, Switzerland
⁷² SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁷³ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁷⁴ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁷⁵ Space Sciences Laboratory, University of California, Berkeley, CA, USA
⁷⁶ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
⁷⁷ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
⁷⁸ Theory Division, PH-TH, CERN, 1211, Geneva 23, Switzerland
⁷⁹ UPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, France
⁸⁰ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
⁸¹ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, Granada, Spain
⁸² University of Granada, Instituto Carlos I de Física Teórica y Computacional, Granada, Spain
⁸³ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 29 June 2014
Accepted: 21 November 2014

Abstract

Any variation in the fundamental physical constants, more particularly in the fine structure constant, α, or in the mass of the electron, m_e, affects the recombination history of the Universe and cause an imprint on the cosmic microwave background angular power spectra. We show that the Planck data allow one to improve the constraint on the time variation of the fine structure constant at redshift z ~ 10³ by about a factor of 5 compared to WMAP data, as well as to break the degeneracy with the Hubble constant, H₀. In addition to α, we can set a constraint on the variation in the mass of the electron, m_e, and in the simultaneous variation of the two constants. We examine in detail the degeneracies between fundamental constants and the cosmological parameters, in order to compare the limits obtained from Planck and WMAP and to determine the constraining power gained by including other cosmological probes. We conclude that independent time variations of the fine structure constant and of the mass of the electron are constrained by Planck to Δα/α = (3.6 ± 3.7) × 10^-3 and Δm_e/m_e = (4 ± 11) × 10^-3 at the 68% confidence level. We also investigate the possibility of a spatial variation of the fine structure constant. The relative amplitude of a dipolar spatial variation in α (corresponding to a gradient across our Hubble volume) is constrained to be δα/α = (−2.4 ± 3.7) × 10^-2.