WMAP precision data enable accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat Ã-dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data. For the WMAP data only, the best-fit parameters are h ¼ 0:72 AE 0:05, b h 2 ¼ 0:024 AE 0:001, m h 2 ¼ 0:14 AE 0:02, ¼ 0:166 þ0:076 À0:071 , n s ¼ 0:99 AE 0:04, and 8 ¼ 0:9 AE 0:1. With parameters fixed only by WMAP data, we can fit finer scale cosmic microwave background (CMB) measurements and measurements of large-scale structure (galaxy surveys and the Ly forest). This simple model is also consistent with a host of other astronomical measurements: its inferred age of the universe is consistent with stellar ages, the baryon/photon ratio is consistent with measurements of the [D/H] ratio, and the inferred Hubble constant is consistent with local observations of the expansion rate. We then fit the model parameters to a combination of WMAP data with other finer scale CMB experiments (ACBAR and CBI), 2dFGRS measurements, and Ly forest data to find the model's best-fit cosmological parameters: WMAP's best determination of ¼ 0:17 AE 0:04 arises directly from the temperaturepolarization (TE) data and not from this model fit, but they are consistent. These parameters imply that the age of the universe is 13:7 AE 0:2 Gyr. With the Ly forest data, the model favors but does not require a slowly varying spectral index. The significance of this running index is sensitive to the uncertainties in the Ly forest.By combining WMAP data with other astronomical data, we constrain the geometry of the universe, tot ¼ 1:02 AE 0:02, and the equation of state of the dark energy, w < À0:78 (95% confidence limit assuming w ! À1). The combination of WMAP and 2dFGRS data constrains the energy density in stable neutrinos: h 2 < 0:0072 (95% confidence limit). For three degenerate neutrino species, this limit implies that their mass is less than 0.23 eV (95% confidence limit). The WMAP detection of early reionization rules out warm dark matter. Subject headings: cosmic microwave background -cosmological parameterscosmology: observations -early universe On-line material: color figure

A simple cosmological model with only six parameters (matter density, m h 2 , baryon density, b h 2 , Hubble constant, H 0 , amplitude of fluctuations, 8 , optical depth, , and a slope for the scalar perturbation spectrum, n s ) fits not only the 3 year WMAP temperature and polarization data, but also small-scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the bestfit values for cosmological parameters for the power-law flat à cold dark matter (ÃCDM) model are ( m h 2 ; b h 2 ; h; n s ; ; 8 ) ¼ (0:1277 þ0:0080 À0:0079 ;0:02229 AE 0:00073;0:732 þ0:031 À0:032 ;0:958 AE 0:016;0:089 AE 0:030; 0:761 þ0:049 À0:048 ). The 3 year data dramatically shrink the allowed volume in this six-dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power-law spectrum, the WMAP data alone require dark matter and favor a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n s ¼ 1; r ¼ 0). Adding additional data sets improves the constraints on these components and the spectral slope. For power-law models, WMAP data alone puts an improved upper limit on the tensor-to-scalar ratio, r 0:002 < 0:65 (95% CL) and the combination of WMAP and the lensing-normalized SDSS galaxy survey implies r 0:002 < 0:30 (95% CL). Models that suppress largescale power through a running spectral index or a large-scale cutoff in the power spectrum are a better fit to the WMAP and small-scale CMB data than the power-law ÃCDM model; however, the improvement in the fit to the WMAP data is only Á 2 ¼ 3 for 1 extra degree of freedom. Models with a running-spectral index are consistent with a higher amplitude of gravity waves. In a flat universe, the combination of WMAP and the Supernova Legacy Survey (SNLS) data yields a significant constraint on the equation of state of the dark energy, w ¼ À0:967 þ0:073 À0:072 . If we assume w ¼ À1, then the deviations from the critical density, K , are small: the combination of WMAP and the SNLS data implies k ¼ À0:011 AE 0:012. The combination of WMAP 3 year data plus the HST Key Project constraint on H 0 implies k ¼ À0:014 AE 0:017 and à ¼ 0:716 AE 0:055. Even if we do not include the prior that the universe is flat, by combining WMAP, large-scale structure, and supernova data, we can still put a strong constraint on the dark energy equation of state, w ¼ À1:08 AE 0:12. For a flat universe, the combination of WMAP and other astronomical data yield a constraint on the sum of the neutrino masses, P m < 0:66 eV (95%CL). Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps using Minkowski functionals, the bispectrum, trispectrum, and a new statistic designed to detect large-scale anisotropies in the fluctuations. Subject headingg s: cosmic microwave background -cosmology: observations

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.

This paper presents the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the Planck spectra at high multipoles ( > ∼ 40) are extremely well described by the standard spatiallyflat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the Planck data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be θ * = (1.04147 ± 0.00062) × 10 −2 , Ω b h 2 = 0.02205 ± 0.00028, Ω c h 2 = 0.1199 ± 0.0027, and n s = 0.9603 ± 0.0073, respectively (note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H 0 = (67.3 ± 1.2) km s −1 Mpc −1 , and a high value of the matter density parameter, Ω m = 0.315 ± 0.017. These values are in tension with recent direct measurements of H 0 and the magnituderedshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using Planck CMB data alone. We use high-resolution CMB data together with Planck to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter ΛCDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured over the standard six-parameter ΛCDM cosmology. The deviation of the scalar spectral index from unity is insensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r 0.002 < 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find N eff = 3.30 ± 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of N eff = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = −1.13 +0.13 −0.10 . We also use the Planck data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter ΛCDM model in describing the Planck data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. T...