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Ade, P.A.R. and Aghanim, N. and Arnaud, M. and Arroja, F. and Ashdown, M. and Aumont, J. and Baccigalupi, C. and Ballardini, M. and Banday, A.J. and Barreiro, R.B. and Bartolo, N. and Battaner, E. and Benabed, K. and Benoît, A. and Benoit-Lévy, A. and Bernard, J.-P. and Bersanelli, M. and Bielewicz, P. and Bock, J.J. and Bonaldi, A. and Bonavera, L. and Bond, J.R. and Borrill, J. and Bouchet, F.R. and Boulanger, F. and Bucher, M. and Burigana, C. and Butler, R.C. and Calabrese, E. and Cardoso, J.-F. and Catalano, A. and Challinor, A. and Chamballu, A. and Chary, R.-R. and Chiang, H.C. and Christensen, P.R. and Church, S. and Clements, D.L. and Colombi, S. and Colombo, L.P.L. and Combet, C. and Contreras, D. and Couchot, F. and Coulais, A. and Crill, B.P. and Curto, A. and Cuttaia, F. and Danese, L. and Davies, R.D. and Davis, R.J. and de Bernardis, P. and de Rosa, A. and de Zotti, G. and Delabrouille, J. and Désert, F.-X. and Diego, J.M. and Dole, H. and Donzelli, S. and Doré, O. and Douspis, M. and Ducout, A. and Dupac, X. and Efstathiou, G. and Elsner, F. and Enßlin, T.A. and Eriksen, H.K. and Fergusson, J. and Finelli⋆, F. and Forni, O. and Frailis, M. and Fraisse, A.A. and Franceschi, E. and Frejsel, A. and Frolov, A. and Galeotta, S. and Galli, S. and Ganga, K. and Gauthier, C. and Giard, M. and Giraud-Héraud, Y. and Gjerløw, E. and González-Nuevo, J. and Górski, K.M. and Gratton, S. and Gregorio, A. and Gruppuso, A. and Gudmundsson, J.E. and Hamann, J. and Handley, W. and Hansen, F.K. and Hanson, D. and Harrison, D.L. and Henrot-Versillé, S. and Hernández-Monteagudo, C. and Herranz, D. and Hildebrandt, S.R. and Hivon, E. and Hobson, M. and Holmes, W.A. and Hornstrup, A. and Hovest, W. and Huang, Z. and Huffenberger, K.M. and Hurier, G. and Jaffe, A.H. and Jaffe, T.R. and Jones, W.C. and Juvela, M. and Keihänen, E. and Keskitalo, R. and Kim, J. and Kisner, T.S. and Kneissl, R. and Knoche, J. and Kunz, M. and Kurki-Suonio, H. and Lagache, G. and Lähteenmäki, A. and Lamarre, J.-M. and Lasenby, A. and Lattanzi, M. and Lawrence, C.R. and Leonardi, R. and Lesgourgues, J. and Levrier, F. and Lewis, A. and Liguori, M. and Lilje, P.B. and Linden-Vørnle, M. and López-Caniego, M. and Lubin, P.M. and Ma, Y.-Z. and Macías-Pérez, J.F. and Maggio, G. and Maino, D. and Mandolesi, N. and Mangilli, A. and Maris, M. and Martin, P.G. and Martínez-González, E. and Masi, S. and Matarrese, S. and McGehee, P. and Meinhold, P.R. and Melchiorri, A. and Mendes, L. and Mennella, A. and Migliaccio, M. and Mitra, S. and Miville-Deschênes, M.-A. and Molinari, D. and Moneti, A. and Montier, L. and Morgante, G. and Mortlock, D. and Moss, Adam and Münchmeyer, M. and Munshi, D. and Murphy, J.A. and Naselsky, P. and Nati, F. and Natoli, P. and Netterfield, C.B. and Nørgaard-Nielsen, H.U. and Noviello, F. and Novikov, D. and Novikov, I. and Oxborrow, C.A. and Paci, F. and Pagano, L. and Pajot, F. and Paladini, R. and Pandolfi, S. and Paoletti, D. and Pasian, F. and Patanchon, G. and Pearson, T.J. and Peiris, H.V. and Perdereau, O. and Perotto, L. and Perrotta, F. and Pettorino, V. and Piacentini, F. and Piat, M. and Pierpaoli, E. and Pietrobon, D. and Plaszczynski, S. and Pointecouteau, E. and Polenta, G. and Popa, L. and Pratt, G.W. and Prézeau, G. and Prunet, S. and Puget, J.-L. and Rachen, J.P. and Reach, W.T. and Rebolo, R. and Reinecke, M. and Remazeilles, M. and Renault, C. and Renzi, A. and Ristorcelli, I. and Rocha, G. and Rosset, C. and Rossetti, M. and Roudier, G. and Rowan-Robinson, M. and Rubiño-Martín, J.A. and Rusholme, B. and Sandri, M. and Santos, D. and Savelainen, M. and Savini, G. and Scott, D. and Seiffert, M. D. and Shellard, E.P.S. and Shiraishi, M. and Spencer, L.D. and Stolyarov, V. and Stompor, R. and Sudiwala, R. and Sunyaev, R. and Sutton, D. and Suur-Uski, A.-S. and Sygnet, J.-F. and Tauber, J.A. and Terenzi, L. and Toffolatti, L. and Tomasi, M. and Tristram, M. and Trombetti, T. and Tucci, M. and Tuovinen, J. and Valenziano, L. and Valiviita, J. and Van Tent, B. and Vielva, P. and Villa, F. and Wade, L.A. and Wandelt, B.D. and Wehus, I.K. and White, M. and Yvon, D. and Zacchei, A. and Zibin, J.P. and Zonca, A. (2016) Planck 2015 results. XX. Constraints on inflation. Astronomy & Astrophysics, 594 . A20/1-A20/65. ISSN 1432-0746

Abstract

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be ns = 0.968 ± 0.006 and tightly constrain its scale dependence to dns/ dlnk = −0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-ℓ polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r0.002< 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r< 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) ∝ φ2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth over the range of scales 0.008 Mpc-1 ≲ k ≲ 0.1 Mpc-1. At large scales, each method finds deviations from a power law, connected to a deficit at multipoles ℓ ≈ 20−40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is | αnon - adi | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum findingthat the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. These results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.

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