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 Ωch2 = 0.120 ± 0.001, baryon density Ωbh2 = 0.0224 ± 0.0001, scalar spectral index ns = 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 Neff = 2.99 ± 0.17, in agreement with the Standard Model prediction Neff = 3.046, and find that the neutrino mass is tightly constrained to ∑mν <  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, ΩK = 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 r0.002 <  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.

We present cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing, using 1321 deg 2 of griz imaging data from the first year of the Dark Energy Survey (DES Y1). We combine three two-point functions: (i) the cosmic shear correlation function of 26 million source galaxies in four redshift bins, (ii) the galaxy angular autocorrelation function of 650,000 luminous red galaxies in five redshift bins, and (iii) the galaxy-shear cross-correlation of luminous red galaxy positions and source galaxy shears. To demonstrate the robustness of these results, we use independent pairs of galaxy shape, photometric-redshift estimation and validation, and likelihood analysis pipelines. To prevent confirmation bias, the bulk of the analysis was carried out while "blind" to the true results; we describe an extensive suite of systematics checks performed and passed during this blinded phase. The data are modeled in flat ΛCDM and wCDM cosmologies, marginalizing over 20 nuisance parameters, varying 6 (for ΛCDM) or 7 (for wCDM) cosmological parameters including the neutrino mass density and including the 457 × 457 element analytic covariance matrix. We find consistent cosmological results from these three two-point functions and from their combination obtain S 8 ≡ σ 8 ðΩ m =0.3Þ 0.5 ¼ 0.773 þ0.026 −0.020 and Ω m ¼ 0.267 þ0.030 −0.017 for ΛCDM; for wCDM, we find S 8 ¼ 0.782 þ0.036 −0.024 , Ω m ¼ 0.284 þ0.033 −0.030 , and w ¼ −0.82 þ0.21 −0.20 at 68% C.L. The precision of these DES Y1 constraints rivals that from the Planck cosmic microwave background measurements, allowing a comparison of structure in the very early and late Universe on equal terms. Although the DES Y1 best-fit values for S 8 and Ω m are lower than the central values from Planck for both ΛCDM and wCDM, the Bayes factor indicates that the DES Y1 and Planck data sets are consistent with each other in the context of ΛCDM. Combining DES Y1 with Planck, baryonic acoustic oscillation measurements from SDSS, 6dF, and BOSS and type Ia supernovae from the Joint Lightcurve Analysis data set, we derive very tight constraints on cosmological parameters: S 8 ¼ 0.802 AE 0.012 and Ω m ¼ 0.298 AE 0.007 in ΛCDM and w ¼ −1.00 þ0.05 −0.04 in wCDM. Upcoming Dark Energy Survey analyses will provide more stringent tests of the ΛCDM model and extensions such as a time-varying equation of state of dark energy or modified gravity.

This work and its companion paper, Amon et al. [Phys. Rev. D 105, 023514 (2022)], present cosmic shear measurements and cosmological constraints from over 100 million source galaxies in the Dark Energy Survey (DES) Year 3 data. We constrain the lensing amplitude parameter S 8 ≡ σ 8 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω m =0.3 p at the 3% level in ΛCDM: S 8 ¼ 0.759 þ0.025 −0.023 (68% CL). Our constraint is at the 2% level when using angular scale cuts that are optimized for the ΛCDM analysis: S 8 ¼ 0.772 þ0.018 −0.017 (68% CL). With cosmic shear alone, we †

This work, together with its companion paper, Secco, Samuroff et al. [Phys. Rev. D 105, 023515 (2022)], present the Dark Energy Survey Year 3 cosmic-shear measurements and cosmological constraints based on an analysis of over 100 million source galaxies. With the data spanning 4143 deg 2 on the sky, divided into four redshift bins, we produce a measurement with a signal-to-noise of 40. We conduct a blind analysis in the context of the Lambda-Cold Dark Matter (ΛCDM) model and find a 3% constraint of the clustering amplitude, S 8 ≡ σ 8 ðΩ m =0.3Þ 0.5 ¼ 0.759 þ0.025 −0.023 . A ΛCDM-Optimized analysis, which safely includes smaller scale information, yields a 2% precision measurement of S 8 ¼ 0.772 þ0.018 −0.017 that is consistent with the fiducial case. The two low-redshift measurements are statistically consistent with the Planck Cosmic Microwave Background result, however, both recovered S 8 values are lower than the highredshift prediction by 2.3σ and 2.1σ (p-values of 0.02 and 0.05), respectively. The measurements are shown to be internally consistent across redshift bins, angular scales and correlation functions. The analysis is demonstrated to be robust to calibration systematics, with the S 8 posterior consistent when varying the choice of redshift calibration sample, the modeling of redshift uncertainty and methodology. Similarly, we find that the corrections included to account for the blending of galaxies shifts our best-fit S 8 by 0.5σ without incurring a substantial increase in uncertainty. We examine the limiting factors for the precision of the cosmological constraints and find observational systematics to be subdominant to the modeling of astrophysics. Specifically, we identify the uncertainties in modeling baryonic effects and intrinsic alignments as the limiting systematics.

We investigate constraints on the Hubble constant (H 0 ) using Baryon Acoustic Oscillations (BAO) and baryon density measurements from Big Bang Nucleosynthesis (BBN). We start by investigating the tension between galaxy BAO measurements and those using the Lyman-α forest, within a Bayesian framework. Using the latest results from eBOSS DR14 we find that the probability of this tension being statistical is 6.3%. We measure H 0 = 67.6±1.1 km s −1 Mpc −1 , with a weak dependence on the BBN prior used, in agreement with results from Planck Cosmic Microwave Background (CMB) results and in strong tension with distance ladder results. Finally, we forecast the future of BAO + BBN measurements of H 0 , using the Dark Energy Spectroscopic Instrument (DESI). We find that the choice of BBN prior will have a significant impact when considering future BAO measurements from DESI.