<i>Planck</i>2013 results. XVI. Cosmological parameters

Abstract

This paper presents the first cosmological results based on &lt;em&gt;Planck&lt;/em&gt; measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the &lt;em&gt;Planck&lt;/em&gt; spectra at high multipoles (&amp;ell; ≳ 40) are extremely well described by the standard spatially-flat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the &lt;em&gt;Planck&lt;/em&gt; data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be θ&lt;sub&gt;&amp;lowast;&lt;/sub&gt; = (1.04147 ± 0.00062) × 10&lt;sup&gt;-2&lt;/sup&gt;, Ω&lt;sub&gt;b&lt;/sub&gt;h&lt;sup&gt;2&lt;/sup&gt; = 0.02205 ± 0.00028, Ω&lt;sub&gt;c&lt;/sub&gt;h&lt;sup&gt;2&lt;/sup&gt; = 0.1199 ± 0.0027, and &lt;em&gt;n&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt; = 0.9603 ± 0.0073, respectively (note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H&lt;sub&gt;0&lt;/sub&gt; = (67.3 ± 1.2) km s&lt;sup&gt;-1&lt;/sup&gt; Mpc&lt;sup&gt;-1&lt;/sup&gt;, and a high value of the matter density parameter, Ω&lt;sub&gt;m&lt;/sub&gt; = 0.315 ± 0.017. These values are in tension with recent direct measurements of H&lt;sub&gt;0&lt;/sub&gt; and the magnitude-redshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using &lt;em&gt;Planck&lt;/em&gt; CMB data alone. We use high-resolution CMB data together with &lt;em&gt;Planck&lt;/em&gt; to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter ΛCDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to &lt;em&gt;Planck&lt;/em&gt; and high-resolution CMB data. None of these models are favoured over the standard six-parameter ΛCDM cosmology. The deviation of the scalar spectral index from unity is insensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r&lt;sub&gt;0.002&lt;/sub&gt; &amp;lt; 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find N&lt;sub&gt;eff&lt;/sub&gt; = 3.30 ± 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of N&lt;sub&gt;eff&lt;/sub&gt; = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = -1.13&lt;sub&gt;-0.10&lt;/sub&gt;&lt;sup&gt;+0.13&lt;/sup&gt;. We also use the &lt;em&gt;Planck&lt;/em&gt; data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter ΛCDM model in describing the &lt;em&gt;Planck&lt;/em&gt; data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. The unusual shape of the spectrum in the multipole range 20 ≲ &amp;ell; ≲ 40 was seen previously in the WMAP data and is a real feature of the primordial CMB anisotropies. The poor fit to the spectrum at low multipoles is not of decisive significance, but is an "anomaly" in an otherwise self-consistent analysis of the &lt;em&gt;Planck&lt;/em&gt; temperature data.

Keywords

Affiliated Institutions

• University of California, Berkeley US
• Université Joseph Fourier FR
• Université Paris Cité FR
• Institute of Astronomy and Astrophysics, Academia Sinica TW
• Jet Propulsion Laboratory US
• Institut National de Physique Nucléaire et de Physique des Particules FR
• Scuola Internazionale Superiore di Studi Avanzati IT
• University of Manchester GB
• Sorbonne Université FR
• California Institute of Technology US
• University College London GB
• Laboratoire de Physique Subatomique et de Cosmologie FR
• University of Toronto CA
• Roche (France) FR
• Istituto Nazionale di Fisica Nucleare, Sezione di Bologna IT
• University of Oslo
• European Space Astronomy Centre ES
• Télécom Paris FR
• Ludwig-Maximilians-Universität München DE
• CEA Paris-Saclay FR
• Sorbonne Paris Cité FR
• Centre National de la Recherche Scientifique FR
• Laboratoire d’Etudes du Rayonnement et de la Matière en Astrophysique et Atmosphères FR
• Universidad de Salamanca ES
• Instituto de Física de Cantabria ES
• Institut d'Astrophysique Spatiale FR
• Osservatorio Astronomico di Padova IT
• Imperial College London GB
• Universidad de Cantabria ES
• Astrophysique, Instrumentation et Modélisation FR
• European Organization for Nuclear Research CH
• McGill University CA
• University of Trieste IT
• Cardiff University GB
• Institut de Planétologie et d'Astrophysique de Grenoble FR
• Trieste Astronomical Observatory IT
• Commissariat à l'Énergie Atomique et aux Énergies Alternatives FR
• Universidad de Granada ES
• University of Ferrara IT
• Université Toulouse III - Paul Sabatier FR
• University of Milan IT
• Lawrence Berkeley National Laboratory US
• University of Cambridge GB
• Université Paris-Sud FR
• Institut Universitaire de France FR
• Laboratoire Traitement et Communication de l’Information FR
• University of Oxford GB
• Infrared Processing and Analysis Center US
• University of KwaZulu-Natal ZA
• European Space Research and Technology Centre NL
• Centro de Estudios de Física del Cosmos de Aragón ES
• Université Grenoble Alpes FR
• Délégation Paris 7 FR
• Max Planck Institute for Astrophysics DE
• Stanford University US
• Institut de Recherche sur les Lois Fondamentales de l'Univers FR
• Institut d'Astrophysique de Paris FR
• Princeton University US
• Sapienza University of Rome IT
• Observatoire de Paris FR
• University of Warsaw PL
• University of Southern California US
• Université Fédérale de Toulouse Midi-Pyrénées FR
• National Institute for Astrophysics IT

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