We present the final nine-year maps and basic results from the Wilkinson Microwave Anisotropy Probe (WMAP) mission. The full nine-year analysis of the time-ordered data provides updated ...characterizations and calibrations of the experiment. We also provide new nine-year full sky temperature maps that were processed to reduce the asymmetry of the effective beams. Temperature and polarization sky maps are examined to separate cosmic microwave background (CMB) anisotropy from foreground emission, and both types of signals are analyzed in detail.We provide new point source catalogs as well as new diffuse and point source foreground masks. An updated template-removal process is used for cosmological analysis; new foreground fits are performed, and new foreground reduced are presented.We nowimplement an optimal C(exp -1)1 weighting to compute the temperature angular power spectrum. The WMAP mission has resulted in a highly constrained Lambda-CDM cosmological model with precise and accurate parameters in agreement with a host of other cosmological measurements. When WMAP data are combined with finer scale CMB, baryon acoustic oscillation, and Hubble constant measurements, we find that big bang nucleosynthesis is well supported and there is no compelling evidence for a non-standard number of neutrino species (N(sub eff) = 3.84 +/- 0.40). The model fit also implies that the age of the universe is (sub 0) = 13.772 +/- 0.059 Gyr, and the fit Hubble constant is H(sub 0) = 69.32 +/- 0.80 km/s/ Mpc. Inflation is also supported: the fluctuations are adiabatic, with Gaussian random phases; the detection of a deviation of the scalar spectral index from unity, reported earlier by the WMAP team, now has high statistical significance (n(sub s) = 0.9608+/-0.0080); and the universe is close to flat/Euclidean (Omega = −0.0027+0.0039/−0.0038). Overall, the WMAP mission has resulted in a reduction of the cosmological parameter volume by a factor of 68,000 for the standard six-parameter Lambda-CDM model, based on CMB data alone. For a model including tensors, the allowed seven-parameter volume has been reduced by a factor 117,000. Other cosmological observations are in accord with the CMB predictions, and the combined data reduces the cosmological parameter volume even further.With no significant anomalies and an adequate goodness of fit, the inflationary flat Lambda-CDM model and its precise and accurate parameters rooted in WMAP data stands as the standard model of cosmology.
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 Delta *LCDM model. The power-law index of the primordial power spectrum is ns = 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, Delta *Sm Delta *n < 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 Yp = 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 21 Delta *s, compared with 13 Delta *s 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 (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.
The WMAP mission has produced sky maps from seven years of observations at L2. We present the angular power spectra derived from the seven-year maps and discuss the cosmological conclusions that can ...be inferred from WMAP data alone. With the seven-year data, the temperature (TT) spectrum measurement has a signal-to-noise ratio per multipole that exceeds unity for l < 919; and in band powers of width Delta *Dl = 10, the signal-to-noise ratio exceeds unity up to l = 1060. The third acoustic peak in the TT spectrum is now well measured by WMAP. In the context of a flat Delta *LCDM model, this improvement allows us to place tighter constraints on the matter density from WMAP data alone, Delta *W m h 2 = 0.1334+0.0056 --0.0055, and on the epoch of matter-radiation equality, z eq = 3196+134 --133. The temperature-polarization (TE) spectrum is detected in the seven-year data with a significance of 20 Delta *s, compared to 13 Delta *s with the five-year data. We now detect the second dip in the TE spectrum near l ~ 450 with high confidence. The TB and EB spectra remain consistent with zero, thus demonstrating low systematic errors and foreground residuals in the data. The low-l EE spectrum, a measure of the optical depth due to reionization, is detected at 5.5 Delta *s significance when averaged over l = 2-7: l(l + 1)C EE l /(2 Delta *p) = 0.074+0.034 --0.025 Delta *mK2 (68% CL). We now detect the high-l, 24 <= l <= 800, EE spectrum at over 8 Delta *s. The BB spectrum, an important probe of gravitational waves from inflation, remains consistent with zero; when averaged over l = 2-7, l(l + 1)C BB l /(2 Delta *p) < 0.055 Delta *mK2 (95% CL). The upper limit on tensor modes from polarization data alone is a factor of two lower with the seven-year data than it was using the five-year data. The data remain consistent with the simple Delta *LCDM model: the best-fit TT spectrum has an effective Delta *y2 of 1227 for 1170 degrees of freedom, with a probability to exceed of 9.6%. The allowable volume in the six-dimensional space of Delta *LCDM parameters has been reduced by a factor of 1.5 relative to the five-year volume, while the Delta *LCDM model that allows for tensor modes and a running scalar spectral index has a factor of three lower volume when fit to the seven-year data. We test the parameter recovery process for bias and find that the scalar spectral index, ns , is biased high, but only by 0.09 Delta *s, while the remaining parameters are biased by <0.15 Delta *s. The improvement in the third peak measurement leads to tighter lower limits from WMAP on the number of relativistic degrees of freedom (e.g., neutrinos) in the early universe: N eff>2.7(95%CL). Also, using WMAP data alone, the primordial helium mass fraction is found to be Y He = 0.28+0.14 --0.15, and with data from higher-resolution cosmic microwave background experiments included, we now establish the existence of pre-stellar helium at >3 Delta *s. These new WMAP measurements provide important tests of big bang cosmology.
New full-sky temperature and polarization maps based on seven years of data from WMAP are presented. The new results are consistent with previous results, but have improved due to reduced noise from ...the additional integration time, improved knowledge of the instrument performance, and improved data analysis procedures. The improvements are described in detail. The seven-year data set is well fit by a minimal six-parameter flat Delta *LCDM model. The parameters for this model, using the WMAP data in conjunction with baryon acoustic oscillation data from the Sloan Digital Sky Survey and priors on H 0 from Hubble Space Telescope observations, are Delta *W b h 2 = 0.02260 ? 0.00053, Delta *W c h 2 = 0.1123 ? 0.0035, Delta *W Delta *L = 0.728+0.015 --0.016, ns = 0.963 ? 0.012, Delta *t = 0.087 ? 0.014, and Delta *s8 = 0.809 ? 0.024 (68% CL uncertainties). The temperature power spectrum signal-to-noise ratio per multipole is greater that unity for multipoles l 919, allowing a robust measurement of the third acoustic peak. This measurement results in improved constraints on the matter density, Delta *W m h 2 = 0.1334+0.0056 --0.0055, and the epoch of matter-radiation equality, z eq = 3196+134 --133, using WMAP data alone. The new WMAP data, when combined with smaller angular scale microwave background anisotropy data, result in a 3 Delta *s detection of the abundance of primordial helium, Y He = 0.326 ? 0.075. When combined with additional external data sets, the WMAP data also yield better determinations of the total mass of neutrinos, Delta *Sm Delta *n <= 0.58 eV(95%CL), and the effective number of neutrino species, N eff = 4.34+0.86 --0.88. The power-law index of the primordial power spectrum is now determined to be ns = 0.963 ? 0.012, excluding the Harrison-Zel'dovich-Peebles spectrum by >3 Delta *s. These new WMAP measurements provide important tests of big bang cosmology.
The Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data provide stringent limits on deviations from the minimal, six-parameter Lambda cold dark matter model. We report these limits and use them ...to constrain the physics of cosmic inflation via Gaussianity, adiabaticity, the power spectrum of primordial fluctuations, gravitational waves, and spatial curvature. We also constrain models of dark energy via its equation of state, parity-violating interaction, and neutrino properties, such as mass and the number of species. We detect no convincing deviations from the minimal model. The six parameters and the corresponding 68% uncertainties, derived from the WMAP data combined with the distance measurements from the Type Ia supernovae (SN) and the Baryon Acoustic Oscillations (BAO) in the distribution of galaxies, are: Omega b h 2 = 0.02267+0.00058 -0.00059, Omega c h 2 = 0.1131 ± 0.0034, Omega Lambda = 0.726 ± 0.015, ns = 0.960 ± 0.013, tau = 0.084 ± 0.016, and at k = 0.002 Mpc-1. From these, we derive sigma 8 = 0.812 ± 0.026, H 0 = 70.5 ± 1.3 km s-1 Mpc-1, Omega b = 0.0456 ± 0.0015, Omega c = 0.228 ± 0.013, Omega m h 2 = 0.1358+0.0037 -0.0036, z reion = 10.9 ± 1.4, and t 0 = 13.72 ± 0.12 Gyr. With the WMAP data combined with BAO and SN, we find the limit on the tensor-to-scalar ratio of r < 0.22(95%CL), and that ns > 1 is disfavored even when gravitational waves are included, which constrains the models of inflation that can produce significant gravitational waves, such as chaotic or power-law inflation models, or a blue spectrum, such as hybrid inflation models. We obtain tight, simultaneous limits on the (constant) equation of state of dark energy and the spatial curvature of the universe: -0.14 < 1 + w < 0.12(95%CL) and -0.0179 < Omega k < 0.0081(95%CL). We provide a set of 'WMAP distance priors,' to test a variety of dark energy models with spatial curvature. We test a time-dependent w with a present value constrained as -0.33 < 1 + w 0 < 0.21 (95% CL). Temperature and dark matter fluctuations are found to obey the adiabatic relation to within 8.9% and 2.1% for the axion-type and curvaton-type dark matter, respectively. The power spectra of TB and EB correlations constrain a parity-violating interaction, which rotates the polarization angle and converts E to B. The polarization angle could not be rotated more than -59 < Delta alpha < 24 (95% CL) between the decoupling and the present epoch. We find the limit on the total mass of massive neutrinos of capital sigma m Delta < 0.67 eV(95%CL), which is free from the uncertainty in the normalization of the large-scale structure data. The number of relativistic degrees of freedom (dof), expressed in units of the effective number of neutrino species, is constrained as N eff = 4.4 ± 1.5 (68%), consistent with the standard value of 3.04. Finally, quantitative limits on physically-motivated primordial non-Gaussianity parameters are -9 < f local NL < 111 (95% CL) and -151 < f equil NL < 253 (95% CL) for the local and equilateral models, respectively.
This paper focuses on cosmological constraints derived from analysis of WMAP data alone. A simple Lambda CDM cosmological model fits the five-year WMAP temperature and polarization data. The basic ...parameters of the model are consistent with the three-year data and now better constrained: Omega b h 2 = 0.02273 ± 0.00062, Omega c h 2 = 0.1099 ± 0.0062, Omega Lambda = 0.742 ± 0.030, ns = 0.963+0.014 -0.015, tau = 0.087 ± 0.017, and sigma 8 = 0.796 ± 0.036, with h = 0.719+0.026 -0.027. With five years of polarization data, we have measured the optical depth to reionization, tau >0, at 5 sigma significance. The redshift of an instantaneous reionization is constrained to be z reion = 11.0 ± 1.4 with 68% confidence. The 2 sigma lower limit is z reion > 8.2, and the 3 sigma limit is z reion > 6.7. This excludes a sudden reionization of the universe at z = 6 at more than 3.5 sigma significance, suggesting that reionization was an extended process. Using two methods for polarized foreground cleaning we get consistent estimates for the optical depth, indicating an error due to the foreground treatment of tau ~ 0.01. This cosmological model also fits small-scale cosmic microwave background (CMB) data, and a range of astronomical data measuring the expansion rate and clustering of matter in the universe. We find evidence for the first time in the CMB power spectrum for a nonzero cosmic neutrino background, or a background of relativistic species, with the standard three light neutrino species preferred over the best-fit Lambda CDM model with N eff = 0 at >99.5% confidence, and N eff > 2.3(95%confidence limit (CL)) when varied. The five-year WMAP data improve the upper limit on the tensor-to-scalar ratio, r < 0.43(95%CL), for power-law models, and halve the limit on r for models with a running index, r < 0.58(95%CL). With longer integration we find no evidence for a running spectral index, with dns /dln k = -0.037 ± 0.028, and find improved limits on isocurvature fluctuations. The current WMAP-only limit on the sum of the neutrino masses is capital sigma m Delta < 1.3 eV(95%CL), which is robust, to within 10%, to a varying tensor amplitude, running spectral index, or dark energy equation of state.
A simple six-parameter Delta *LCDM model provides a successful fit to WMAP data. This holds both when the WMAP data are analyzed alone or in combination with other cosmological data. Even so, it is ...appropriate to examine the data carefully to search for hints of deviations from the now standard model of cosmology, which includes inflation, dark energy, dark matter, baryons, and neutrinos. The cosmological community has subjected the WMAP data to extensive and varied analyses. While there is widespread agreement as to the overall success of the six-parameter Delta *LCDM model, various 'anomalies' have been reported relative to that model. In this paper we examine potential anomalies and present analyses and assessments of their significance. In most cases we find that claimed anomalies depend on posterior selection of some aspect or subset of the data. Compared with sky simulations based on the best-fit model, one can select for low probability features of the WMAP data. Low probability features are expected, but it is not usually straightforward to determine whether any particular low probability feature is the result of the a posteriori selection or non-standard cosmology. Hypothesis testing could, of course, always reveal an alternative model that is statistically favored, but there is currently no model that is more compelling. We find that two cold spots in the map are statistically consistent with random cosmic microwave background (CMB) fluctuations. We also find that the amplitude of the quadrupole is well within the expected 95% confidence range and therefore is not anomalously low. We find no significant anomaly with a lack of large angular scale CMB power for the best-fit Delta *LCDM model. We examine in detail the properties of the power spectrum data with respect to the Delta *LCDM model and find no significant anomalies. The quadrupole and octupole components of the CMB sky are remarkably aligned, but we find that this is not due to any single map feature; it results from the statistical combination of the full-sky anisotropy fluctuations. It may be due, in part, to chance alignments between the primary and secondary anisotropy, but this only shifts the coincidence from within the last scattering surface to between it and the local matter density distribution. While this alignment appears to be remarkable, there was no model that predicted it, nor has there been a model that provides a compelling retrodiction. We examine claims of a hemispherical or dipole power asymmetry across the sky and find that the evidence for these claims is not statistically significant. We confirm the claim of a strong quadrupolar power asymmetry effect, but there is considerable evidence that the effect is not cosmological. The likely explanation is an insufficient handling of beam asymmetries. We conclude that there is no compelling evidence for deviations from the Delta *LCDM model, which is generally an acceptable statistical fit to WMAP and other cosmological data.
We present new full-sky temperature and polarization maps in five frequency bands from 23 to 94 GHz, based on data from the first five years of the Wilkinson Microwave Anisotropy Probe (WMAP) sky ...survey. The new maps are consistent with previous maps and are more sensitive. The five-year maps incorporate several improvements in data processing made possible by the additional years of data and by a more complete analysis of the instrument calibration and in-flight beam response. We present several new tests for systematic errors in the polarization data and conclude that W-band polarization data is not yet suitable for cosmological studies, but we suggest directions for further study. We do find that Ka-band data is suitable for use; in conjunction with the additional years of data, the addition of Ka band to the previously used Q- and V-band channels significantly reduces the uncertainty in the optical depth parameter, tau . Further scientific results from the five-year data analysis are presented in six companion papers and are summarized in Section 7 of this paper. With the five-year WMAP data, we detect no convincing deviations from the minimal six-parameter Lambda CDM model: a flat universe dominated by a cosmological constant, with adiabatic and nearly scale-invariant Gaussian fluctuations. Using WMAP data combined with measurements of Type Ia supernovae and Baryon Acoustic Oscillations in the galaxy distribution, we find (68% CL uncertainties): Omega b h 2 = 0.02267+0.00058 -0.00059, Omega c h 2 = 0.1131 ± 0.0034, Omega Lambda = 0.726 ± 0.015, ns = 0.960 ± 0.013, tau = 0.084 ± 0.016, and at k = 0.002 Mpc-1. From these we derive sigma 8 = 0.812 ± 0.026, H 0 = 70.5 ± 1.3 km s-1 Mpc-1, Omega b = 0.0456 ± 0.0015, Omega c = 0.228 ± 0.013, Omega m h 2 = 0.1358+0.0037 -0.0036, z reion = 10.9 ± 1.4, and t 0 = 13.72 ± 0.12 Gyr. The new limit on the tensor-to-scalar ratio is r < 0.22(95%CL), while the evidence for a running spectral index is insignificant, dns /dln k = -0.028 ± 0.020 (68% CL). We obtain tight, simultaneous limits on the (constant) dark energy equation of state and the spatial curvature of the universe: -0.14 < 1 + w < 0.12(95%CL) and -0.0179 < Omega k < 0.0081(95%CL). The number of relativistic degrees of freedom, expressed in units of the effective number of neutrino species, is found to be N eff = 4.4 ± 1.5 (68% CL), consistent with the standard value of 3.04. Models with N eff = 0 are disfavored at >99.5% confidence. Finally, new limits on physically motivated primordial non-Gaussianity parameters are -9 < f local NL < 111 (95% CL) and -151 < f equil NL < 253 (95% CL) for the local and equilateral models, respectively.
A simple cosmological model with only six parameters (matter density, Omega sub(m)h super(2), baryon density, Omega sub(b)h super(2), Hubble constant, H sub(0), amplitude of fluctuations, sigma ...sub(8), optical depth, tau , and a slope for the scalar perturbation spectrum, n sub(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 best-fit values for cosmological parameters for the power-law flat Lambda cold dark matter ( Lambda CDM) model are ( Omega sub(m)h super(2), Omega sub(b)h super(2),h,n sub(s), tau , sigma sub(8)) = (0.1277 super(+0.0080)-0.0079,0.02229 plus or minus 0.00073,0.732 super(+0.031)-0.032,0.958 plus or minus 0.016,0.089 plus or minus 0.030,0.761 super(+0.049)-0.048). The 3 year data dramatically shrink the allowed volume in mis 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 sub(s) = 1, r = 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 sub(0.002) < 0.65 (95% CL) and the combination of WMAP and the lensing-normalized SDSS galaxy survey implies r sub(0.002) < 0.30 (95% CL). Models that suppress large-scale 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 Lambda CDM model; however, the improvement in the fit to the WMAP data is only Delta chi super(2) = 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 = -0.967 super(+0.073)-0.072. If we assume w = -1, then the deviations from the critical density, Omega sub(K) are small: the combination of WMAP and the SNLS data implies Omega sub(k) = -0.011 plus or minus 0.012. The combination of WMAP 3 year data plus the HST Key Project constraint on H sub(0) implies Omega sub(k) = -0.014 plus or minus 0.017 and Omega sub( Lambda ) = 0.716 plus or minus 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 = -1.08 plus or minus 0.12. For a flat universe, the combination of WMAP and other astronomical data yield a constraint on the sum of the neutrino masses, capital sigma m sub( upsilon ) < 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.
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