[Paper Review] Planck 2018 results. VI. Cosmological parameters

Planck Collaboration, N. Aghanim+180 more|arXiv (Cornell University)|Jul 17, 2018

Cosmology and Gravitation TheoriesPhysics and Astronomy402 references3,576 citations

TL;DR

This paper presents the final Planck 2018 cosmological parameter constraints from full-mission cosmic microwave background (CMB) temperature and polarization anisotropies, combined with lensing reconstruction. It confirms the base ΛCDM model with high precision, yielding H₀ = 67.4 ± 0.5 km s⁻¹ Mpc⁻¹, σ₈ = 0.811 ± 0.006, and τ = 0.054 ± 0.007, while revealing persistent tensions with local H₀ measurements and some large-scale structure data.

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 $ au = 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 $100 heta_*=1.0411\pm 0.0003$. 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 $N_{ m eff} = 2.99\pm 0.17$, and the neutrino mass is tightly constrained to $\sum m_ u< 0.12$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)

Motivation & Objective

• To deliver the final, high-precision cosmological parameter constraints from the full Planck mission CMB data set.
• To test the robustness of the base ΛCDM model using temperature, polarization, and lensing data in combination.
• To investigate tensions between Planck results and external data sets, particularly local H₀ measurements and DES galaxy clustering.
• To constrain extensions to ΛCDM, including dark energy, neutrino masses, extra relativistic species, and primordial non-Gaussianity.
• To assess internal consistency of the CMB data across multipoles and lensing reconstruction.

Proposed method

• Utilizes full-mission Planck temperature and polarization maps (TT, TE, EE) across 30–2900 MHz, with improved low-ℓ and high-ℓ likelihoods.
• Employs the Plik, CamSpec, and low-ℓ likelihoods for temperature and polarization power spectra, with careful modeling of beam and beam transfer functions.
• Applies a CMB lensing likelihood derived from the lensing potential reconstruction, using quadratic estimators and calibration from simulations.
• Performs joint Bayesian parameter estimation using Monte Carlo Markov Chain (MCMC) sampling with the CosmoMC and MontePython frameworks.
• Tests model extensions via grid-based and parameterized likelihood scans, including w₀, wa, Neff, mν, and primordial tensor-to-scalar ratio r.
• Combines Planck data with external probes: BAO (e.g., BOSS, SDSS), Type Ia supernovae (Pantheon), and weak lensing (DES) for joint constraints.

Experimental results

Research questions

• RQ1 What are the most precise constraints on the base ΛCDM parameters from the full Planck CMB data set?
• RQ2 How do Planck's CMB measurements compare with local H₀ measurements, and what is the significance of the tension?
• RQ3 To what extent do Planck data support extensions to ΛCDM, such as non-zero neutrino masses, extra relativistic species, or dark energy dynamics?
• RQ4 Is there evidence for deviations from a purely power-law primordial scalar spectrum or from the standard value of Neff = 3.046?
• RQ5 How consistent are the high-ℓ and low-ℓ CMB power spectra, and what does lensing reconstruction reveal about potential systematic effects?

Key findings

• The base ΛCDM model is strongly consistent with Planck data, yielding a Hubble constant H₀ = 67.4 ± 0.5 km s⁻¹ Mpc⁻¹, matter density Ωₘ = 0.315 ± 0.007, and σ₈ = 0.811 ± 0.006.
• The optical depth to reionization is measured as τ = 0.054 ± 0.007, with improved precision from enhanced large-scale polarization data.
• The scalar spectral index is constrained to ns = 0.965 ± 0.004, and the angular acoustic scale is measured at 100θ* = 1.0411 ± 0.0003 with 0.03% precision.
• The effective number of relativistic species is Neff = 2.99 ± 0.17 (including BAO), consistent with the standard model prediction of 3.046.
• Neutrino mass is tightly constrained: ∑mν < 0.12 eV at 95% confidence, with no evidence for degenerate active neutrinos.
• The dark energy equation of state is w₀ = −1.03 ± 0.03 when combined with BAO and SNe data, consistent with a cosmological constant.
• A 3.6σ tension remains with local H₀ measurements (Riess et al. 2019), and no simple model extension resolves it within Planck's data.
• BBN predictions for helium and deuterium abundances are in excellent agreement with observations under the Planck base-ΛCDM model.
• No evidence is found for primordial non-Gaussianity, tensor modes (r₀.₀₀₂ < 0.06), or massive sterile neutrinos.