<i>Planck</i>2013 results. XXII. Constraints on inflation
P. A. R. AdeSchool of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UKN. AghanimInstitut d'Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, FranceC. Armitage-CaplanSub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UKM. ArnaudLaboratoire AIM, IRFU/Service d'Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, FranceM. AshdownKavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UKF. Atrio‐BarandelaDepartamento de Física Fundamental, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, SpainJ. AumontInstitut d'Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, FranceC. BaccigalupiSISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, ItalyA. J. BandayUniversité de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, FranceR. B. BarreiroInstituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, SpainJ. G. BartlettJet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USAN. BartoloDipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, ItalyE. BattanerUniversity of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18071 Granada, SpainK. BenabedInstitut d'Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, FranceA. Benoı̂tUPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, FranceA. Benoit-LévyDepartment of Physics and Astronomy, University College London, London WC1E 6BT, UKJ.-P. BernardUniversité de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, FranceM. BersanelliDipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, ItalyP. BielewiczSISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, ItalyJ. BobinLaboratoire AIM, IRFU/Service d'Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, FranceJ. J. BockCalifornia Institute of Technology, Pasadena, California, USAA. BonaldiJodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UKJ. R. BondCITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, CanadaJ. BorrillSpace Sciences Laboratory, University of California, Berkeley, California, USAF. R. BouchetInstitut d'Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, FranceM. BridgesAstrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UKM. BucherAPC, 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, FranceC. BuriganaINAF/IASF Bologna, via Gobetti 101, 40129 Bologna, ItalyR. C. ButlerINAF/IASF Bologna, via Gobetti 101, 40129 Bologna, ItalyE. CalabreseSub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UKJ.-F. CardosoAPC, 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, FranceA. CatalanoLERMA, CNRS, Observatoire de Paris, 61 avenue de l'Observatoire, 75014 Paris, FranceA. ChallinorInstitute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UKA. ChamballuDSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, FranceH. C. ChiangAstrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, 4000 Durban, South AfricaL.-Y ChiangInstitute of Astronomy and Astrophysics, Academia Sinica, 10617 Taipei, TaiwanP. R. ChristensenS. ChurchStanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USAD. L. ClementsImperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UKS. ColombiUPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, FranceL. P. L. ColomboJet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USAF. CouchotLAL, Université Paris-Sud, CNRS/IN2P3, Orsay, FranceA. CoulaisLERMA, CNRS, Observatoire de Paris, 61 avenue de l'Observatoire, 75014 Paris, FranceB. P. CrillJet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USAA. CurtoAstrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UKF. CuttaiaINAF/IASF Bologna, via Gobetti 101, 40129 Bologna, ItalyL. DaneseSISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, ItalyR. D. DaviesJodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UKR. J. DavisJodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UKP. de BernardisDipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00185 Roma, ItalyA. de RosaINAF/IASF Bologna, via Gobetti 101, 40129 Bologna, ItalyG. de ZottiINAF – Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, 35122 Padova, ItalyJ. DelabrouilleAPC, 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, FranceJ.‐M. DelouisUPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, FranceF.–X. DésertIPAG: Institut de Planétologie et d'Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, FranceC. DickinsonJodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UKJ. M. DiegoInstituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, SpainH. DoleInstitut d'Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, FranceS. DonzelliINAF/IASF Milano, via E. Bassini 15, 20133 Milano, ItalyO. DoréCalifornia Institute of Technology, Pasadena, California, USAM. DouspisInstitut d'Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, FranceJ. DunkleySub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UKX. DupacEuropean Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, SpainG. EfstathiouInstitute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UKT. A. EnßlinMax-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, GermanyH. K. EriksenInstitute of Theoretical Astrophysics, University of Oslo, Blindern, 0315 Oslo, NorwayF. Finelli⋆INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, ItalyO. ForniCNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, FranceM. FrailisINAF – Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34131 Trieste, ItalyE. FranceschiINAF/IASF Bologna, via Gobetti 101, 40129 Bologna, ItalyS. GaleottaINAF – Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34131 Trieste, ItalyK. GangaAPC, 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, FranceC. GauthierAPC, 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, FranceM. GiardCNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, FranceG. GiardinoEuropean Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The NetherlandsY. Giraud–HéraudAPC, 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, FranceJ. González-NuevoInstituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, SpainK. M. GórskiJet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USAS. GrattonKavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UKA. GregorioINAF – Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34131 Trieste, ItalyA. GruppusoINAF/IASF Bologna, via Gobetti 101, 40129 Bologna, ItalyJ. HamannTheory Division, PH-TH, CERN, 1211 Geneva 23, SwitzerlandF. K. HansenInstitute of Theoretical Astrophysics, University of Oslo, Blindern, 0315 Oslo, NorwayD. HansonMcGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, CanadaD. L. HarrisonInstitute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UKS. Henrot–VersilléLAL, Université Paris-Sud, CNRS/IN2P3, Orsay, FranceC. Hernández-MonteagudoMax-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, GermanyD. HerranzInstituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, SpainS. R. HildebrandtCalifornia Institute of Technology, Pasadena, California, USAE. HivonInstitut d'Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, FranceM. HobsonAstrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UKW. A. HolmesJet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USAA. HornstrupDTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, DenmarkW. HovestMax-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, GermanyK. M. HuffenbergerDepartment of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USAA. H. JaffeImperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UKT. R. JaffeCNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, FranceW. C. JonesDepartment of Physics, Princeton University, Princeton, New Jersey, USAM. JuvelaDepartment of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, FinlandE. KeihänenDepartment of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland
2014en
ABI
Annotatsiya
We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be ns = 0.9603 ± 0.0073, ruling out exact scale invariance at over 5 s. Planck establishes an upper bound on the tensor-to-scalar ratio of r< 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V>< 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n = 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dns/dlnk =-0.0134 ± 0.0090. We verify these conclusions through a numerical analysis, which makes no slow-roll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by 2eff 10 ; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on fNL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the 2eff by approximately 4 as a result of slightly lowering the theoretical prediction for the l40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.
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