Planck intermediate results

LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological 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 African Institute for Mathematical Sciences, 6-8 Melrose Road, Muizenberg, 7945 Cape Town, South Africa
³ Agenzia Spaziale Italiana Science Data Center, via del Politecnico snc, 00133 Roma, Italy
⁴ Agenzia Spaziale Italiana, via del Politecnico snc, 00133 Roma, Italy
⁵ Aix Marseille Univ., CNRS, LAM, Laboratoire d’Astrophysique de Marseille, 13013 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, Durban 4000, 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, CA 91125, USA
¹¹ Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹² Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, California, CA 94720, USA
¹³ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
¹⁴ Département de Physique Théorique, Université de Genève, 24 Quai E. Ansermet, 1211 Genève 4, Switzerland
¹⁵ Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
¹⁶ Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain
¹⁷ Department of Astrophysics/IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, The Netherlands
¹⁸ Department of Mathematics, University of Stellenbosch, Stellenbosch 7602, South Africa
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 of Sussex, Brighton BN1 9QH, UK
²² Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00014 Helsinki, Finland
²³ Department of Physics, Princeton University, Princeton, New Jersey, NJ 08544, USA
²⁴ Department of Physics, University of California, Berkeley, California, CA 94607, USA
²⁵ Department of Physics, University of California, One Shields Avenue, Davis, California, CA 95616, USA
²⁶ Department of Physics, University of California, Santa Barbara, California, CA 93106, USA
²⁷ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, IL 61820, USA
²⁸ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
²⁹ Dipartimento di Fisica e Astronomia, Alma Mater Studiorum, Università degli Studi di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
³⁰ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³¹ Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
³² Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, Italy
³³ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
³⁴ Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00133 Roma, Italy
³⁵ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, UrbanizaciónVillafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
³⁶ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
³⁷ Gran Sasso Science Institute, INFN, viale F. Crispi 7, 67100 L’ Aquila, Italy
³⁸ HGSFP and University of Heidelberg, Theoretical Physics Department, Philosophenweg 16, 69120 Heidelberg, Germany
³⁹ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, Pennsylvania, PA 19041, USA
⁴⁰ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁴¹ INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁴² INAF–Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 40127 Trieste, Italy
⁴³ INAF/IASF Bologna, via Gobetti 101, 40129 Bologna, Italy
⁴⁴ INAF/IASF Milano, via E. Bassini 15, 20133 Milano, Italy
⁴⁵ INFN – CNAF, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁶ INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁷ INFN, Sezione di Ferrara, via Saragat 1, 44122 Ferrara, Italy
⁴⁸ INFN, Sezione di Roma 2, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00185 Roma, Italy
⁴⁹ INFN/National Institute for Nuclear Physics, via Valerio 2, 34127 Trieste, Italy
⁵⁰ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁵¹ Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405 Orsay Cedex, France
⁵² Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98bis Boulevard Arago, 75014 Paris, France
⁵³ Institute Lorentz, Leiden University, PO Box 9506, Leiden 2300 RA, The Netherlands
⁵⁴ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁵⁵ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0371 Oslo, Norway
⁵⁶ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, 38205 Tenerife, Spain
⁵⁷ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁵⁸ Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
⁵⁹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, CA 91125, USA
⁶⁰ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁶¹ Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
⁶² Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁶³ LAL, Université Paris-Sud, CNRS/IN2P3, 91898 Orsay, France
⁶⁴ LERMA, CNRS, Observatoire de Paris, 61 Avenue de l’Observatoire, 75014 Paris, France
⁶⁵ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁶⁶ Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53, rue des Martyrs, 38026 Grenoble Cedex, France
⁶⁷ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁶⁸ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁶⁹ Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, 00076 Aalto, Finland
⁷⁰ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁷¹ Mullard Space Science Laboratory, University College London, Surrey RH5 6NT, UK
⁷² Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warsaw, Poland
⁷³ Nordita (Nordic Institute for Theoretical Physics), Roslagstullsbacken 23, 106 91 Stockholm, Sweden
⁷⁴ Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, PR China
⁷⁵ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁷⁶ San Diego Supercomputer Center, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
⁷⁷ School of Chemistry and Physics, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban, 4000, South Africa
⁷⁸ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁷⁹ School of Physics and Astronomy, Sun Yat-Sen University, 135 Xingang Xi Road, Guangzhou, 510006, PR China
⁸⁰ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁸¹ School of Physics, Indian Institute of Science Educationand Research Thiruvananthapuram (IISER-TVM), Trivandrum 695016, Kerala, India
⁸² Simon Fraser University, Department of Physics, 8888 University Drive, Burnaby BC, Canada
⁸³ Sorbonne Université-UPMC, UMR 7095, Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁸⁴ Sorbonne Universités, Institut Lagrange de Paris (ILP), 98bis Boulevard Arago, 75014 Paris, France
⁸⁵ Space Sciences Laboratory, University of California, Berkeley, California, CA 94720, USA
⁸⁶ The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, 106 91 Stockholm, Sweden
⁸⁷ UPMC Univ. Paris 06, UMR 7095, 98bis Boulevard Arago, 75014 Paris, France
⁸⁸ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
⁸⁹ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18071 Granada, Spain
⁹⁰ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

^⋆ Corresponding authors: Silvia Galli, e-mail: gallis@iap.fr; Marius Millea, e-mail: millea@iap.fr

Received: 8 August 2016
Accepted: 10 September 2017

Abstract

The six parameters of the standard ΛCDM model have best-fit values derived from the Planck temperature power spectrum that are shifted somewhat from the best-fit values derived from WMAP data. These shifts are driven by features in the Planck temperature power spectrum at angular scales that had never before been measured to cosmic-variance level precision. We have investigated these shifts to determine whether they are within the range of expectation and to understand their origin in the data. Taking our parameter set to be the optical depth of the reionized intergalactic medium τ, the baryon density ω_b, the matter density ω_m, the angular size of the sound horizon θ_∗, the spectral index of the primordial power spectrum, n_s, and A_se^{− 2τ} (where A_s is the amplitude of the primordial power spectrum), we have examined the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment ℓ < 800 in the Planck temperature power spectrum) and an all angular-scale data set (ℓ < 2500Planck temperature power spectrum), each with a prior on τ of 0.07 ± 0.02. We find that the shifts, in units of the 1σ expected dispersion for each parameter, are { Δτ,ΔA_se^{− 2τ},Δn_s,Δω_m,Δω_b,Δθ_∗ } = { −1.7,−2.2,1.2,−2.0,1.1,0.9 }, with a χ² value of 8.0. We find that this χ² value is exceeded in 15% of our simulated data sets, and that a parameter deviates by more than 2.2σ in 9% of simulated data sets, meaning that the shifts are not unusually large. Comparing ℓ < 800 instead to ℓ> 800, or splitting at a different multipole, yields similar results. We examined the ℓ < 800 model residuals in the ℓ> 800 power spectrum data and find that the features there that drive these shifts are a set of oscillations across a broad range of angular scales. Although they partly appear similar to the effects of enhanced gravitational lensing, the shifts in ΛCDM parameters that arise in response to these features correspond to model spectrum changes that are predominantly due to non-lensing effects; the only exception is τ, which, at fixed A_se^{− 2τ}, affects the ℓ> 800 temperature power spectrum solely through the associated change in A_s and the impact of that on the lensing potential power spectrum. We also ask, “what is it about the power spectrum at ℓ < 800 that leads to somewhat different best-fit parameters than come from the full ℓ range?” We find that if we discard the data at ℓ < 30, where there is a roughly 2σ downward fluctuation in power relative to the model that best fits the full ℓ range, the ℓ < 800 best-fit parameters shift significantly towards the ℓ < 2500 best-fit parameters. In contrast, including ℓ < 30, this previously noted “low-ℓ deficit” drives n_s up and impacts parameters correlated with n_s, such as ω_m and H₀. As expected, the ℓ < 30 data have a much greater impact on the ℓ < 800 best fit than on the ℓ < 2500 best fit. So although the shifts are not very significant, we find that they can be understood through the combined effects of an oscillatory-like set of high-ℓ residuals and the deficit in low-ℓ power, excursions consistent with sample variance that happen to map onto changes in cosmological parameters. Finally, we examine agreement between PlanckTT data and two other CMB data sets, namely the Planck lensing reconstruction and the TT power spectrum measured by the South Pole Telescope, again finding a lack of convincing evidence of any significant deviations in parameters, suggesting that current CMB data sets give an internally consistent picture of the ΛCDM model.