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

The combination of seven-year data from WMAP and improved astrophysical data rigorously tests the standard cosmological model and places new constraints on its basic parameters and extensions. By combining the WMAP data with the latest distance measurements from the baryon acoustic oscillations (BAO) in the distribution of galaxies and the Hubble constant (H 0 ) measurement, we determine the parameters of the simplest six-parameter ΛCDM model. The power-law index of the primordial power spectrum is n s = 0.968 ± 0.012 (68% CL) for this data combination, a measurement that excludes the Harrison-Zel'dovich-Peebles spectrum by 99.5% CL. The other parameters, including those beyond the minimal set, are also consistent with, and improved from, the five-year results. We find no convincing deviations from the minimal model. The seven-year temperature power spectrum gives a better determination of the third acoustic peak, which results in a better determination of the redshift of the matter-radiation equality epoch. Notable examples of improved parameters are the total mass of neutrinos, m ν < 0.58 eV (95% CL), and the effective number of neutrino species, N eff = 4.34 +0.86 −0.88 (68% CL), which benefit from better determinations of the third peak and H 0 . The limit on a constant dark energy equation of state parameter from WMAP+BAO+H 0 , without high-redshift Type Ia supernovae, is w = −1.10 ± 0.14 (68% CL). We detect the effect of primordial helium on the temperature power spectrum and provide a new test of big bang nucleosynthesis by measuring Y p = 0.326 ± 0.075 (68% CL). We detect, and show on the map for the first time, the tangential and radial polarization patterns around hot and cold spots of temperature fluctuations, an important test of physical processes at z = 1090 and the dominance of adiabatic scalar fluctuations. The seven-year polarization data have significantly improved: we now detect the temperature-E-mode polarization cross power spectrum at 21σ , compared with 13σ from the five-year data. With the seven-year temperature-B-mode cross power spectrum, the limit on a rotation of the polarization plane due to potential parity-violating effects has improved by 38% to Δα = −1.• 1 ± 1.• 4(statistical) ± 1.• 5(systematic) (68% CL). We report significant detections of the Sunyaev-Zel'dovich (SZ) effect at the locations of known clusters of galaxies. The measured SZ signal agrees well with the expected signal from the X-ray data on a cluster-by-cluster basis. However, it is a factor of 0.5-0.7 times the predictions from "universal profile" of Arnaud et al., analytical models, and hydrodynamical simulations. We find, for the first time in the SZ effect, a significant difference between the cooling-flow and non-cooling-flow clusters (or relaxed and non-relaxed clusters), which can explain some of the discrepancy. This lower amplitude is consistent with the lower-than-theoretically expected SZ power spectrum recently measured by the South Pole Telescope Collaboration.

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 constraints based on the final nine-year WMAP data, in conjunction with a number of additional cosmological data sets. The WMAP data alone, and in combination, continue to be remarkably well fit by a six-parameter ΛCDM model. When WMAP data are combined with measurements of the high-l cosmic microwave background (CMB) anisotropy, the baryon acoustic oscillation (BAO) scale, and the Hubble constant, the matter and energy densities, Ω b h 2 , Ω c h 2 , and Ω Λ , are each determined to a precision of ∼1.5%. The amplitude of the primordial spectrum is measured to within 3%, and there is now evidence for a tilt in the primordial spectrum at the 5σ level, confirming the first detection of tilt based on the five-year WMAP data. At the end of the WMAP mission, the nine-year data decrease the allowable volume of the six-dimensional ΛCDM parameter space by a factor of 68,000 relative to pre-WMAP measurements. We investigate a number of data combinations and show that their ΛCDM parameter fits are consistent. New limits on deviations from the six-parameter model are presented, for example: the fractional contribution of tensor modes is limited to r < 0.13 (95% CL); the spatial curvature parameter is limited to Ω k = −0.0027 +0.0039 −0.0038 ; the summed mass of neutrinos is limited to m ν < 0.44 eV (95% CL); and the number of relativistic species is found to lie within N eff = 3.84 ± 0.40, when the full data are analyzed. The joint constraint on N eff and the primordial helium abundance, Y He , agrees with the prediction of standard Big Bang nucleosynthesis. We compare recent Planck measurements of the Sunyaev-Zel'dovich effect with our seven-year measurements, and show their mutual agreement. Our analysis of the polarization pattern around temperature extrema is updated. This confirms a fundamental prediction of the standard cosmological model and provides a striking illustration of acoustic oscillations and adiabatic initial conditions in the early universe. 18 The map resolution levels refer to the HEALPix pixelization scheme (Gorski et al. 2005) where r4, r5, r9, and r10 refer to N side values of 16, 32, 512, and 1024, respectively. 19 these codes are available at http://lambda.gsfc.nasa.gov

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We describe our methodology for comparing the Wilkinson Microwave Anisotropy Probe (WMAP) measurements of the cosmic microwave background (CMB) and other complementary data sets to theoretical models. The unprecedented quality of the WMAP data and the tight constraints on cosmological parameters that are derived require a rigorous analysis so that the approximations made in the modeling do not lead to significant biases. We describe our use of the likelihood function to characterize the statistical properties of the microwave background sky. We outline the use of the Monte Carlo Markov Chains to explore the likelihood of the data given a model to determine the best-fit cosmological parameters and their uncertainties. We add to the WMAP data the 'e700 Cosmic Background Imager (CBI) and Arcminute Cosmology Bolometer Array Receiver (ACBAR) measurements of the CMB, the galaxy power spectrum at z $ 0 obtained from the Two-Degree Field Galaxy Redshift Survey (2dFGRS), and the matter power spectrum at z $ 3 as measured with the Ly forest. These last two data sets complement the CMB measurements by probing the matter power spectrum of the nearby universe. Combining CMB and 2dFGRS requires that we include in our analysis a model for galaxy bias, redshift distortions, and the nonlinear growth of structure. We show how the statistical and systematic uncertainties in the model and the data are propagated through the full analysis.

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