Planck 2018 results. VI. Cosmological parameters

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)

• The paper refines the standard ΛCDM model parameters, reporting H0 = 67.36 ± 0.54 km/s/Mpc and Ωm = 0.315 ± 0.0073 with advanced CMB data analyses.
• It employs sophisticated temperature, polarization, and lensing reconstruction methods to ensure robust cross-validation across various datasets.
• The findings highlight minor tensions with local H0 measurements, indicating the need for further investigation into potential systematic effects and model extensions.

Analytical Overview of "Planck 2018 Results: Cosmological Parameters"

The Planck Collaboration's 2018 release presents a comprehensive re-examination of cosmological parameters derived from full-mission data of the cosmic microwave background (CMB) anisotropies, leveraging advanced methods in both polarization and temperature analysis, as well as lensing reconstruction. Rather than introducing new paradigms, this paper fortifies the $\Lambda$CDM model and refines previously established measurements, offering increased precision and evaluating extensions to the standard model.

The key findings demonstrate high consistency with a six-parameter $\Lambda$CDM model, which assumes a spatially-flat Universe with adiabatic initial conditions. The data robustly constrain the Hubble constant $$H_0 = 67.36 \pm 0.54 \, \text{km.s}^{-1}.\text{Mpc}^{-1}$$ and matter density $\Omega_m = 0.315\pm 0.0073$. These findings remain stable across various dataset combinations and potential model extensions. Additionally, the measurements refine the optical depth to reionization $\tau = 0.0544 \pm 0.0073$, which in turn sharpens constraints on correlated parameters like the scalar spectral index $n_s$ and the primordial amplitude $A_s$.

The data indicate a stronger gravitational lensing amplitude than predicted, albeit consistent with a $\Lambda$CDM cosmology, resolved by incorporating small fluctuations in parameter domains rather than systemic deviations. Notably, the results highlight tensions with local $H_0$ measurements, suggesting further scrutiny in astrophysical model parameters.

Analysis of one-parameter extensions to $\Lambda$CDM, including variations in curvature, neutrino mass ($\Sigma m_\nu < 0.12\, \text{eV}$) and effective relativistic species (constrained to $N_{\text{eff}} = 2.99\pm 0.34$), shows no compelling evidence for model deviation. Moreover, testing for early Universe parameters suggested no significant isocurvature or non-Gaussian effects, aligning with single-field inflation predictions.

The report underscores the Planck satellite's critical role in CMB analysis: critically refining cosmological parameters, evaluating extensions of $\Lambda$CDM, and serving as a baseline for subsequent CMB experiments. While largely supporting $\Lambda$CDM, slight tensions, particularly with local $H_0$ measurements, underline the need for new theoretical insights or potentially undiscovered systematic errors.

In the field of future observational cosmology, the Planck 2018 results provide a high-precision scaffold upon which contemporary and next-generation surveys, such as those from DESI and LSST, will build, potentially resolving current tensions and probing beyond the scope of standard cosmological models. Further engagement with cross-collaborative datasets could provide clarity on the minor, yet potentially insightful, anomalies noted in this comprehensive cosmological analysis.