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arxiv: 1807.06209 · v4 · submitted 2018-07-17 · 🌌 astro-ph.CO

Planck 2018 results. VI. Cosmological parameters

Planck Collaboration: N. Aghanim , Y. Akrami , M. Ashdown , J. Aumont , C. Baccigalupi , M. Ballardini , A. J. Banday , R. B. Barreiro
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N. Bartolo S. Basak R. Battye K. Benabed J.-P. Bernard M. Bersanelli P. Bielewicz J. J. Bock J. R. Bond J. Borrill F. R. Bouchet F. Boulanger M. Bucher C. Burigana R. C. Butler E. Calabrese J.-F. Cardoso J. Carron A. Challinor H. C. Chiang J. Chluba L. P. L. Colombo C. Combet D. Contreras B. P. Crill F. Cuttaia P. De Bernardis G. de Zotti J. Delabrouille J.-M. Delouis E. Di Valentino J. M. Diego O. Dor\'e M. Douspis A. Ducout X. Dupac S. Dusini G. Efstathiou F. Elsner T. A. En{\ss}lin H. K. Eriksen Y. Fantaye M. Farhang J. Fergusson R. Fernandez-Cobos F. Finelli F. Forastieri M. Frailis A. A. Fraisse E. Franceschi A. Frolov S. Galeotta S. Galli K. Ganga R. T. G\'enova-Santos M. Gerbino T. Ghosh J. Gonz\'alez-Nuevo K. M. G\'orski S. Gratton A. Gruppuso J. E. Gudmundsson J. Hamann W. Handley F. K. Hansen D. Herranz S. R. Hildebrandt E. Hivon Z. Huang A. H. Jaffe W. C. Jones A. Karakci E. Keih\"anen R. Keskitalo K. Kiiveri J. Kim T. S. Kisner L. Knox N. Krachmalnicoff M. Kunz H. Kurki-Suonio G. Lagache J.-M. Lamarre A. Lasenby M. Lattanzi C. R. Lawrence M. Le Jeune P. Lemos J. Lesgourgues F. Levrier A. Lewis M. Liguori P. B. Lilje M. Lilley V. Lindholm M. L\'opez-Caniego P. M. Lubin Y.-Z. Ma J. F. Mac\'ias-P\'erez G. Maggio D. Maino N. Mandolesi A. Mangilli A. Marcos-Caballero M. Maris P. G. Martin M. Martinelli E. Mart\'inez-Gonz\'alez S. Matarrese N. Mauri J. D. McEwen P. R. Meinhold A. Melchiorri A. Mennella M. Migliaccio M. Millea S. Mitra M.-A. Miville-Desch\^enes D. Molinari L. Montier G. Morgante A. Moss P. Natoli H. U. N{\o}rgaard-Nielsen L. Pagano D. Paoletti B. Partridge G. Patanchon H. V. Peiris F. Perrotta V. Pettorino F. Piacentini L. Polastri G. Polenta J.-L. Puget J. P. Rachen M. Reinecke M. Remazeilles A. Renzi G. Rocha C. Rosset G. Roudier J. A. Rubi\~no-Mart\'in B. Ruiz-Granados L. Salvati M. Sandri M. Savelainen D. Scott E. P. S. Shellard C. Sirignano G. Sirri L. D. Spencer R. Sunyaev A.-S. Suur-Uski J. A. Tauber D. Tavagnacco M. Tenti L. Toffolatti M. Tomasi T. Trombetti L. Valenziano J. Valiviita B. Van Tent L. Vibert P. Vielva F. Villa N. Vittorio B. D. Wandelt I. K. Wehus M. White S. D. M. White A. Zacchei A. Zonca
This is my paper

Pith reviewed 2026-05-10 14:36 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords cosmological parametersCMB anisotropiesLambda CDM modeldark matter densitybaryon densityHubble constantneutrino massPlanck mission
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The pith

Planck's final CMB measurements fix the standard flat six-parameter Lambda CDM parameters to high precision and find no compelling evidence for extensions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reports cosmological parameters from the complete set of Planck satellite observations of cosmic microwave background anisotropies. The data show strong consistency with the spatially flat six-parameter Lambda cold dark matter model when analyzed separately in temperature, polarization, and lensing channels and in combination. Derived values include a dark matter density of 0.120 plus or minus 0.001, baryon density of 0.0224 plus or minus 0.0001, scalar spectral index of 0.965 plus or minus 0.004, and optical depth of 0.054 plus or minus 0.007, with the angular acoustic scale determined to 0.03 percent precision. Inferred late-universe quantities such as the Hubble constant equal 67.4 plus or minus 0.5 kilometers per second per megaparsec under the base model. Combining with baryon acoustic oscillation data further constrains extra relativistic degrees of freedom to 2.99 plus or minus 0.17 and the sum of neutrino masses below 0.12 electronvolts while leaving the base model intact.

Core claim

A combined analysis gives dark matter density Omega_c h squared equal to 0.120 plus or minus 0.001, baryon density Omega_b h squared equal to 0.0224 plus or minus 0.0001, scalar spectral index n_s equal to 0.965 plus or minus 0.004, and optical depth tau equal to 0.054 plus or minus 0.007. We find good consistency with the standard spatially-flat six-parameter Lambda CDM cosmology having a power-law spectrum of adiabatic scalar perturbations from polarization, temperature, and lensing, separately and in combination. These results are only weakly dependent on the cosmological model and remain stable with somewhat increased errors in many commonly considered extensions. We find no compelling证据

What carries the argument

The likelihood fit of the observed CMB temperature, polarization, and lensing power spectra to the six-parameter base Lambda CDM model while marginalizing over standard foreground contributions.

If this is right

  • The Hubble constant is inferred to be 67.4 plus or minus 0.5 km/s/Mpc, the matter density parameter 0.315 plus or minus 0.007, and the fluctuation amplitude sigma_8 0.811 plus or minus 0.006 under the base model.
  • Extra relativistic degrees of freedom are limited to N_eff equal to 2.99 plus or minus 0.17 when the CMB results are combined with baryon acoustic oscillation data.
  • The sum of neutrino masses is constrained below 0.12 eV at 95 percent .
  • A mild preference for higher lensing amplitude appears in the spectra but is not supported by the lensing reconstruction or by baryon acoustic oscillation data in extended models.
  • The angular acoustic scale 100 theta_star is measured as 1.0411 plus or minus 0.0003.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These parameter values supply a fixed benchmark that future large-scale structure surveys can use to test whether apparent tensions with local distance measurements persist.
  • The reported optical depth and spectral index place direct limits on the epoch of reionization and the simplest single-field inflation models.
  • If the mild lensing amplitude preference grows with improved data, it could motivate targeted searches for scale-dependent modifications to gravity or clustering.
  • The tight neutrino mass bound can be combined with terrestrial oscillation experiments to narrow the allowed mass hierarchy.

Load-bearing premise

The observed CMB power spectra are produced by the base spatially flat six-parameter Lambda CDM model plus standard foregrounds with no large unmodeled systematics or new physics that would change the shape of the likelihood surface.

What would settle it

An independent measurement from galaxy clustering or distance-ladder methods that yields a Hubble constant differing from 67.4 kilometers per second per megaparsec by many times the stated uncertainty while the CMB spectra themselves remain unchanged would falsify the consistency of the base model.

read the original abstract

We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter $\Lambda$CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base $\Lambda$CDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density $\Omega_c h^2 = 0.120\pm 0.001$, baryon density $\Omega_b h^2 = 0.0224\pm 0.0001$, scalar spectral index $n_s = 0.965\pm 0.004$, and optical depth $\tau = 0.054\pm 0.007$ (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 $100\theta_*=1.0411\pm 0.0003$. 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-$\Lambda$CDM cosmology, the inferred late-Universe parameters are: Hubble constant $H_0 = (67.4\pm 0.5)$km/s/Mpc; matter density parameter $\Omega_m = 0.315\pm 0.007$; and matter fluctuation amplitude $\sigma_8 = 0.811\pm 0.006$. We find no compelling evidence for extensions to the base-$\Lambda$CDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be $N_{\rm eff} = 2.99\pm 0.17$, and the neutrino mass is tightly constrained to $\sum m_\nu< 0.12$eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -$\Lambda$CDM at over $2\,\sigma$, which pulls some parameters that affect the lensing amplitude away from the base-$\Lambda$CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper presents cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. It finds good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ω_c h² = 0.120±0.001, baryon density Ω_b h² = 0.0224±0.0001, scalar spectral index n_s = 0.965±0.004, and optical depth τ = 0.054±0.007. The angular acoustic scale is measured to 0.03% precision. The paper reports no compelling evidence for extensions to the base-ΛCDM model, with constraints on N_eff and neutrino mass when combined with BAO. It notes a >2σ preference for higher lensing amplitudes in the spectra but not supported by lensing reconstruction or BAO.

Significance. If the results hold, this is a landmark paper providing the definitive constraints on cosmological parameters from Planck CMB data. It demonstrates strong internal consistency and external cross-checks. The explicit acknowledgment of the lensing amplitude tension without claiming new physics is a positive aspect. The stability of the base model parameters under extensions and the tight bounds on additional parameters like neutrino mass add to its significance. This work sets the standard for ΛCDM parameters and has high impact in the field.

minor comments (2)
  1. [Abstract] Abstract: The quoted 0.03% precision on the angular acoustic scale (100θ_* = 1.0411 ± 0.0003) is a key result; the main text should explicitly reference the table or section deriving this quantity to aid readers.
  2. [Lensing discussion] Lensing amplitude discussion: The >2σ preference for higher lensing amplitudes is noted but would benefit from a direct cross-reference to the specific figure or table showing the deviation and its impact on parameters.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. The referee's summary correctly reflects the main results, including the consistency with base-ΛCDM, the quoted parameter values, and the discussion of the lensing amplitude preference.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's derivation consists of standard likelihood maximization of the base flat ΛCDM model against the Planck temperature, polarization, and lensing spectra, yielding the quoted parameter values as direct fit outputs. Independent lensing reconstruction and external BAO constraints are invoked as cross-checks that do not reduce to the same fitted quantities by construction. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations that collapse the central claim are present; the analysis remains externally falsifiable against the observed data and separate probes.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the CMB data are generated by the standard flat ΛCDM model with adiabatic scalar perturbations; the six parameters are fitted quantities whose values constitute the result rather than independent inputs.

free parameters (1)
  • Ω_c h², Ω_b h², n_s, τ, H_0, A_s (or equivalent)
    The six base-ΛCDM parameters are determined by fitting the theoretical power spectra to the measured CMB data.
axioms (2)
  • domain assumption The universe is spatially flat and described by the 6-parameter ΛCDM model with a power-law spectrum of adiabatic scalar perturbations.
    Invoked throughout the base-model analysis and extension tests.
  • domain assumption Foreground contamination and instrumental systematics are adequately modeled by the chosen templates and masks.
    Required for the likelihood to be interpreted as cosmological.

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