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Planck 2018 results. VI. Cosmological parameters

Aghanim, N. and Ghosh, T. and Bock, J. J. and Crill, B. P. and Doré, O. and Hildebrandt, S. R. and Rocha, G. and Górski, K. M. and Lawrence, C. R. and Mitra, S. and Roudier, G. (2020) Planck 2018 results. VI. Cosmological parameters. Astronomy and Astrophysics, 641 . Art. No. A6. ISSN 0004-6361.

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We present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ω_ch² = 0.120 ± 0.001, baryon density Ω_bh² = 0.0224 ± 0.0001, scalar spectral index n_s = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ* = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H₀ = (67.4 ± 0.5)  km s⁻¹ Mpc⁻¹; matter density parameter Ωm = 0.315 ± 0.007; and matter fluctuation amplitude σ₈ = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be N_(eff) = 2.99 ± 0.17, in agreement with the Standard Model prediction N_(eff) = 3.046, and find that the neutrino mass is tightly constrained to ∑m_ν <  0.12  eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, Ω_K = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w₀ = −1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r_(0.002) <  0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6σ, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Aghanim, N.0000-0002-6688-8992
Bock, J. J.0000-0002-5710-5212
Crill, B. P.0000-0002-4650-8518
Doré, O.0000-0002-5009-7563
Hildebrandt, S. R.0000-0003-0220-0009
Rocha, G.0000-0002-4150-8076
Górski, K. M.0000-0003-2933-8630
Roudier, G.0000-0002-7402-7797
Additional Information:© 2020 ESO. Article published by EDP Sciences. Received 20 July 2018; Accepted 20 March 2020; Published online 11 September 2020. 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 We additionally acknowledge support from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007- 2013)/ERC Grant Agreement No. [616170]. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 725456, CMBSPEC). We thank Ofelia Pisanti for providing updated numerical BBN results from the PArthENoPE code, Cyril Pitrou for producing some results from the PRIMAT code, and the DES team for sharing their likelihoods. We also thank Marco Crisostomi, Ignacy Sawicky, Alessandra Silvestri, and Filippo Vernizzi for discussions on the dark-energy and modified-gravity models. Some of the results in this paper have been derived using the HEALPix package.
Errata:Planck 2018 results - VI. Cosmological parameters (Corrigendum). Planck Collaboration, N. Aghanim, et. al., A&A, 652 (2021) C4; DOI:
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
Partnership for Advanced Computing in Europe (PRACE)UNSPECIFIED
European Research Council (ERC)616170
European Research Council (ERC)725456
Subject Keywords:cosmic background radiation – cosmological parameters
Record Number:CaltechAUTHORS:20191002-090602025
Persistent URL:
Official Citation:Planck 2018 results - VI. Cosmological parameters. Planck Collaboration, N. Aghanim, et. al., A&A, 641 (2020) A6; DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99005
Deposited By: Tony Diaz
Deposited On:02 Oct 2019 16:46
Last Modified:11 Aug 2021 22:42

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