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Planck 2018 results. X. Constraints on inflation

Akrami, Y. and Ghosh, T. and Bock, J. J. and Crill, B. P. and Doré, O. and Rocha, G. M. and Górski, K. M. and Lawrence, C. R. and Mitra, S. and Roudier, G. and Wehus, I. K. (2020) Planck 2018 results. X. Constraints on inflation. Astronomy and Astrophysics, 641 . Art. No. A10. ISSN 0004-6361.

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We report on the implications for cosmic inflation of the 2018 release of the Planck cosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be n_s = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence of n_s, either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combining Planck with a compilation of baryon acoustic oscillation data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, r_(0.002) <  0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r_(0.002) <  0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential, V″(ϕ) < 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005 Mpc⁻¹ ≲ k ≲ 0.2 Mpc⁻¹. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectra. For the case of oscillatory features that are logarithmic or linear in k, this result is further strengthened by a new combined analysis including the Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively. Planck power spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Akrami, Y.0000-0002-2407-7956
Bock, J. J.0000-0002-5710-5212
Crill, B. P.0000-0002-4650-8518
Doré, O.0000-0002-5009-7563
Rocha, G. M.0000-0002-4150-8076
Additional Information:© 2020 Planck Collaboration. Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Received 17 July 2018; Accepted 19 August 2019; Published online 11 September 2020. Planck ( is a project of the European Space Agency (ESA) with instruments provided by two scientific consortia funded by ESA member states and led by Principal Investigators from France and Italy, telescope reflectors provided through a collaboration between ESA and a scientific consortium led and funded by Denmark, and additional contributions from NASA (USA). We are grateful to Jan Hamann and Jim Zibin for extensive help with the final editing of this manuscript. 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
Group:Astronomy Department
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
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
Spanish Supercomputing Network (RES)UNSPECIFIED
Ministry of Employment and the Economy (Finland)UNSPECIFIED
Academy of FinlandUNSPECIFIED
Finnish IT Center for Science (CSC)UNSPECIFIED
Deutsches Zentrum für Luft- und Raumfahrt (DLR)UNSPECIFIED
Max Planck SocietyUNSPECIFIED
Canadian Space Agency (CSA)UNSPECIFIED
State Secretariat for Education and Research (Switzerland)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
Partnership for Advanced Computing in Europe (PRACE)UNSPECIFIED
Subject Keywords:inflation – cosmic background radiation
Record Number:CaltechAUTHORS:20190925-124312083
Persistent URL:
Official Citation:Planck 2018 results - X. Constraints on inflation. Planck Collaboration, Y. Akrami, et. al., A&A, 641 (2020) A10; DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98858
Deposited By: Tony Diaz
Deposited On:25 Sep 2019 21:15
Last Modified:14 Sep 2020 17:35

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