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Planck 2018 results: VI. Cosmological parameters

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Planck Collaboration, Aghanim, N., Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J. +174 more·2020·Astronomy & Astrophysics
DOI 10.1051/0004-6361/201833910
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Abstract

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 0.5 σ 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 c h 2 = 0.120 ± 0.001, baryon density Ω b h 2 = 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 100 θ * = 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 H 0 = (67.4 ± 0.5) km s −1 Mpc −1 ; matter density parameter Ω m = 0.315 ± 0.007; and matter fluctuation amplitude σ 8 = 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 2 σ , 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 w 0 = −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, 3.6 σ , 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.

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  • Any background-level departure from ΛCDM changes both distances and growth, so late-time parameter inferences are in principle sensitive to these dynamics.

    “Any background-level departure from ΛCDM changes both distances and growth, so late-time parameter inferences are in principle sensitive to these dynamics [1].”

    From Dynamical systems analysis of an Einstein–Cartan ekpyrotic nonsingular bounce cosmology (2026) · cites this paper as [1]

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Authors
Planck Collaboration, Aghanim, N., Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., Basak, S., Battye, R., Benabed, K., Bernard, J.-P., Bersanelli, M., Bielewicz, P., Bock, J. J., Bond, J. R., Borrill, J., Bouchet, F. R., Boulanger, F., Bucher, M., Burigana, C., Butler, R. C., Calabrese, E., Cardoso, J.-F., Carron, J., Challinor, A., Chiang, H. C., Chluba, J., Colombo, L. P. L., Combet, C., Contreras, D., Crill, B. P., Cuttaia, F., de Bernardis, P., de Zotti, G., Delabrouille, J., Delouis, J.-M., Di Valentino, E., Diego, J. M., Doré, O., Douspis, M., Ducout, A., Dupac, X., Dusini, S., Efstathiou, G., Elsner, F., Enßlin, T. A., Eriksen, H. K., Fantaye, Y., Farhang, M., Fergusson, J., Fernandez-Cobos, R., Finelli, F., Forastieri, F., Frailis, M., Fraisse, A. A., Franceschi, E., Frolov, A., Galeotta, S., Galli, S., Ganga, K., Génova-Santos, R. T., Gerbino, M., Ghosh, T., González-Nuevo, J., Górski, K. M., Gratton, S., Gruppuso, A., Gudmundsson, J. E., Hamann, J., Handley, W., Hansen, F. K., Herranz, D., Hildebrandt, S. R., Hivon, E., Huang, Z., Jaffe, A. H., Jones, W. C., Karakci, A., Keihänen, E., Keskitalo, R., Kiiveri, K., Kim, J., Kisner, T. S., Knox, L., Krachmalnicoff, N., Kunz, M., Kurki-Suonio, H., Lagache, G., Lamarre, J.-M., Lasenby, A., Lattanzi, M., Lawrence, C. R., Le Jeune, M., Lemos, P., Lesgourgues, J., Levrier, F., Lewis, A., Liguori, M., Lilje, P. B., Lilley, M., Lindholm, V., López-Caniego, M., Lubin, P. M., Ma, Y.-Z., Macías-Pérez, J. F., Maggio, G., Maino, D., Mandolesi, N., Mangilli, A., Marcos-Caballero, A., Maris, M., Martin, P. G., Martinelli, M., Martínez-González, E., Matarrese, S., Mauri, N., McEwen, J. D., Meinhold, P. R., Melchiorri, A., Mennella, A., Migliaccio, M., Millea, M., Mitra, S., Miville-Deschênes, M.-A., Molinari, D., Montier, L., Morgante, G., Moss, A., Natoli, P., Nørgaard-Nielsen, H. U., Pagano, L., Paoletti, D., Partridge, B., Patanchon, G., Peiris, H. V., Perrotta, F., Pettorino, V., Piacentini, F., Polastri, L., Polenta, G., Puget, J.-L., Rachen, J. P., Reinecke, M., Remazeilles, M., Renzi, A., Rocha, G., Rosset, C., Roudier, G., Rubiño-Martín, J. A., Ruiz-Granados, B., Salvati, L., Sandri, M., Savelainen, M., Scott, D., Shellard, E. P. S., Sirignano, C., Sirri, G., Spencer, L. D., Sunyaev, R., Suur-Uski, A.-S., Tauber, J. A., Tavagnacco, D., Tenti, M., Toffolatti, L., Tomasi, M., Trombetti, T., Valenziano, L., Valiviita, J., Van Tent, B., Vibert, L., Vielva, P., Villa, F., Vittorio, N., Wandelt, B. D., Wehus, I. K., White, M., White, S. D. M., Zacchei, A., & Zonca, A.
Affiliations
  • Université Paris-Sud (FR)
  • Leiden University (NL)
  • University of Cambridge (GB)
  • Université Toulouse III - Paul Sabatier (FR)
  • Scuola Internazionale Superiore di Studi Avanzati (IT)
  • Osservatorio di Astrofisica e Scienza dello Spazio (IT)
  • Centre National de la Recherche Scientifique (FR)
  • Universidad de Cantabria (ES)
  • University of Padua (IT)
  • Indian Institute of Science Education and Research Thiruvananthapuram (IN)
  • University of Manchester (GB)
  • University of Milan (IT)
  • California Institute of Technology (US)
  • University of Toronto (CA)
  • Lawrence Berkeley National Laboratory (US)
  • University of Ferrara (IT)
  • Cardiff University (GB)
  • University of Sussex (GB)
  • Princeton University (US)
  • University of British Columbia (CA)
  • Kavli Institute for the Physics and Mathematics of the Universe (JP)
  • European Space Agency (FR)
  • Istituto Nazionale di Fisica Nucleare, Sezione di Padova (IT)
  • Max Planck Institute for Astrophysics (DE)
  • University of Oslo (NO)
  • African Institute for Mathematical Sciences (ZA)
  • Shahid Beheshti University (IR)
  • Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (IT)
  • Trieste Astronomical Observatory (IT)
  • Simon Fraser University (CA)
  • Universidad de La Laguna (ES)
  • Argonne National Laboratory (US)
  • Universidad de Oviedo (ES)
  • Stockholm University (SE)
  • UNSW Sydney (AU)
  • Sun Yat-sen University (CN)
  • Imperial College London (GB)
  • University of Helsinki (FI)
  • University of California, Davis (US)
  • University of California, Santa Barbara (US)
  • Purple Mountain Observatory (CN)
  • Heidelberg University (DE)
  • University College London (GB)
  • Istituto Nazionale di Fisica Nucleare, Sezione di Roma I (IT)
  • University of Rome Tor Vergata (IT)
  • University of Nottingham (GB)
  • DTU Space (DK)
  • Haverford College (US)
  • Sapienza University of Rome (IT)
  • Agenzia Spaziale Italiana (IT)
  • Radboud University Nijmegen (NL)
  • Russian Academy of Sciences (RU)
  • University of Trieste (IT)
  • Istituto Nazionale di Fisica Nucleare, Centro Nazionale Analisi Fotogrammi (IT)
  • Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara (IT)
  • San Diego Supercomputer Center (US)
ORCID
Venue
Astronomy & Astrophysics
Publisher
EDP Sciences
Published
2020-09
Volume
641
Pages
A6
ISSN
  • 0004-6361 (ISSN-L)
  • 1432-0746
DOI
10.1051/0004-6361/201833910
OpenAlex
W4288079944
Cited by
14,258
References
17
Citations by year
2026: 1929 · 2025: 3023 · 2024: 2694 · 2023: 2302 · 2022: 2116 · 2021: 1739 · 2020: 446 · 2019: 6 · 2018: 1
FWCI
740.89
Type
journal article
Language
en
Open access
Licence
www.edpsciences.org/en/authors/copyright-and-licensing (vor, 10 d)
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  • Figshare (submittedVersion)
  • IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion)
  • UCrea (University of Cantabria) (submittedVersion, cc-by)
  • Radboud Repository (Radboud University) (submittedVersion)
  • UWC Research Repository (University of the Western Cape) (submittedVersion)
  • Spiral (Imperial College London) (submittedVersion)
  • Padua Research Archive (University of Padova) (submittedVersion, cc-by)
  • Radboud Repository (Radboud University) (submittedVersion, other-oa)
Funders
  • National Aeronautics and Space Administration
  • UK Space Agency
  • European Commission (2007–2013, HORIZON2020, FP/2007-2013)/ERC, FP/2007/2013)
  • Science Foundation Ireland
  • Agence Nationale de la Recherche (ANR-16-IDEX-0008)
  • Partnership for Advanced Computing in Europe AISBL
  • Centre National d’Etudes Spatiales (IN2P3)
  • Tekes
  • Max-Planck-Gesellschaft
  • China Scholarship Council
  • Centre National de la Recherche Scientifique
  • Ministério da Ciência, Tecnologia e Ensino Superior
  • Science and Technology Facilities Council (IN2P3)
  • Fundação para a Ciência e a Tecnologia
  • Institut National de Physique Nucléaire et de Physique des Particules
  • H2020 European Research Council (725456)
  • FP7 Ideas: European Research Council (616170)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
Keywords
Planck 2018, cosmic microwave background anisotropies, cosmological parameters, CMB polarization, lensing reconstruction, reionization optical depth, dark matter density, baryon density, scalar spectral index, Hubble constant, matter density parameter, amplitude of matter fluctuations, effective number of relativistic species, neutrino mass

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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