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Planck 2015 results. XX. Constraints on inflation

Ade, P. A. R. and Bock, J. J. and Crill, B. P. and Doré, O. and Hildebrandt, S. R. and Pearson, T. J. and Prézeau, G. and Rocha, G. and Seiffert, M. D. and Chary, R.-R. and McGehee, P. and Paladini, R. and Rusholme, B. (2016) Planck 2015 results. XX. Constraints on inflation. Astronomy and Astrophysics, 594 . Art. No. A20. ISSN 0004-6361.

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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 r_(0.002)< 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) ∝ φ^2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R^2 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 P_R(k) 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 | α_(non – 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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Doré, O.0000-0002-5009-7563
Pearson, T. J.0000-0001-5213-6231
Chary, R.-R.0000-0001-7583-0621
Additional Information:© 2016 ESO. Received: 14 February 2015; Accepted: 3 March 2016; Published online 20 September 2016. The Planck Collaboration acknowledges the support of: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231. Part of this work was undertaken at the STFC DiRAC HPC Facilities at the University of Cambridge, funded by UK BIS National E-infrastructure capital grants. We gratefully acknowledge the IN2P3 Computer Center ( for providing a significant amount of the computing resources and services needed for this work.
Group:Infrared Processing and Analysis Center (IPAC), COSMOS
Funding AgencyGrant Number
European Space Agency (ESA)UNSPECIFIED
Centre National d'Études Spatiales (CNES)UNSPECIFIED
Centre National de la Recherche Scientifique (CNRS)UNSPECIFIED
Institut National des Sciences de l'Univers (INSU)UNSPECIFIED
Institut National de Physique Nucléaire et de Physique des Particules (IN2P3)UNSPECIFIED
Institut National du Patrimoine (INP)UNSPECIFIED
Agenzia Spaziale Italiana (ASI)UNSPECIFIED
Consiglio Nazionale delle Ricerche (CNR)UNSPECIFIED
Istituto Nazionale di Astrofisica (INAF)UNSPECIFIED
Department of Energy (DOE)UNSPECIFIED
Science and Technology Facilities Council (STFC)UNSPECIFIED
United Kingdom Space Agency (UKSA)UNSPECIFIED
Consejo Superior de Investigaciones Científicas (CSIC)UNSPECIFIED
Ministerio de Economía, Industria y Competitividad (MINECO)UNSPECIFIED
Junta de AndalucíaUNSPECIFIED
Finnish Funding Agency for Technology and Innovation (Tekes)UNSPECIFIED
Academy of FinlandUNSPECIFIED
Finnish IT Center for Science (CSC)UNSPECIFIED
Deutschen Zentrums für Luft- und Raumfahrt (DLR)UNSPECIFIED
Canadian Space Agency (CSA)UNSPECIFIED
State Secretariat for Education, Research and Innovation (SER)UNSPECIFIED
Swiss Space Office (SSO)UNSPECIFIED
Research Council of NorwayUNSPECIFIED
Science Foundation, IrelandUNSPECIFIED
Fundação para a Ciência e a Tecnologia (FCT)UNSPECIFIED
Ministério da Ciência, Tecnologia e Ensino Superior (MCTES)UNSPECIFIED
European Research Council (ERC)UNSPECIFIED
Department of Energy (DOE)DE-AC02-05CH11231
UK BIS National E-InfrastructureUNSPECIFIED
Subject Keywords:cosmic background radiation / cosmology: theory / early Universe / inflation
Record Number:CaltechAUTHORS:20170222-105731785
Persistent URL:
Official Citation:Planck 2015 results - XX. Constraints on inflation Planck Collaboration, P. A. R. Ade, N. Aghanim, M. Arnaud, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, E. Battaner, K. Benabed, A. Benoît, A. Benoit-Lévy, J.-P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, A. Bonaldi, L. Bonavera, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J.-F. Cardoso, A. Catalano, A. Challinor, A. Chamballu, R.-R. Chary, H. C. Chiang, P. R. Christensen, S. Church, D. L. Clements, S. Colombi, L. P. L. Colombo, C. Combet, D. Contreras, F. Couchot, A. Coulais, B. P. Crill, A. Curto, F. Cuttaia, L. Danese, R. D. Davies, R. J. Davis, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, F.-X. Désert, J. M. Diego, H. Dole, S. Donzelli, O. Doré, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, J. Fergusson, F. Finelli⋆, O. Forni, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frejsel, A. Frolov, S. Galeotta, S. Galli, K. Ganga, C. Gauthier, M. Giard, Y. Giraud-Héraud, E. Gjerløw, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gregorio, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Hanson, D. L. Harrison, S. Henrot-Versillé, C. Hernández-Monteagudo, D. Herranz, S. R. Hildebrandt, E. Hivon, M. Hobson, W. A. Holmes, A. Hornstrup, W. Hovest, Z. Huang, K. M. Huffenberger, G. Hurier, A. H. Jaffe, T. R. Jaffe, W. C. Jones, M. Juvela, E. Keihänen, R. Keskitalo, J. Kim, T. S. Kisner, R. Kneissl, J. Knoche, M. Kunz, H. Kurki-Suonio, G. Lagache, A. Lähteenmäki, J.-M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, R. Leonardi, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Linden-Vørnle, M. López-Caniego, P. M. Lubin, Y.-Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, M. Maris, P. G. Martin, E. Martínez-González, S. Masi, S. Matarrese, P. McGehee, P. R. Meinhold, A. Melchiorri, L. Mendes, A. Mennella, M. Migliaccio, S. Mitra, M.-A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, D. Mortlock, A. Moss, M. Münchmeyer, D. Munshi, J. A. Murphy, P. Naselsky, F. Nati, P. Natoli, C. B. Netterfield, H. U. Nørgaard-Nielsen, F. Noviello, D. Novikov, I. Novikov, C. A. Oxborrow, F. Paci, L. Pagano, F. Pajot, R. Paladini, S. Pandolfi, D. Paoletti, F. Pasian, G. Patanchon, T. J. Pearson, H. V. Peiris, O. Perdereau, L. Perotto, F. Perrotta, V. Pettorino, F. Piacentini, M. Piat, E. Pierpaoli, D. Pietrobon, S. Plaszczynski, E. Pointecouteau, G. Polenta, L. Popa, G. W. Pratt, G. Prézeau, S. Prunet, J.-L. Puget, J. P. Rachen, W. T. Reach, R. Rebolo, M. Reinecke, M. Remazeilles, C. Renault, A. Renzi, I. Ristorcelli, G. Rocha, C. Rosset, M. Rossetti, G. Roudier, M. Rowan-Robinson, J. A. Rubiño-Martín, B. Rusholme, M. Sandri, D. Santos, M. Savelainen, G. Savini, D. Scott, M. D. Seiffert, E. P. S. Shellard, M. Shiraishi, L. D. Spencer, V. Stolyarov, R. Stompor, R. Sudiwala, R. Sunyaev, D. Sutton, A.-S. Suur-Uski, J.-F. Sygnet, J. A. Tauber, L. Terenzi, L. Toffolatti, M. Tomasi, M. Tristram, T. Trombetti, M. Tucci, J. Tuovinen, L. Valenziano, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, L. A. Wade, B. D. Wandelt, I. K. Wehus, M. White, D. Yvon, A. Zacchei, J. P. Zibin and A. Zonca A&A, 594 (2016) A20 DOI:
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ID Code:74467
Deposited By: Tony Diaz
Deposited On:22 Feb 2017 19:21
Last Modified:22 Feb 2017 19:21

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