J. L. Weiland

SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP *) OBSERVATIONS: COSMOLOGICAL INTERPRETATION

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 (H0) measurement, we determine the parameters of the simplest six-parameter ΛCDM 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, � mν < 0.58 eV (95% CL), and the effective number of neutrino species, Neff = 4.34 +0.86 −0.88 (68% CL), which benefit from better determinations of the third peak and H0. The limit on a constant dark energy equation of state parameter from WMAP+BAO+H0, 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 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.

First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters

WMAP precision data enable accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat � -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 � 0:05, � bh 2 ¼ 0:024 � 0:001, � mh 2 ¼ 0:14 � 0:02, � ¼ 0:166 þ0:076 � 0:071 , ns ¼ 0:99 � 0:04, and � 8 ¼ 0:9 � 0:1. With parameters fixed only by WMAP data, we can fit finer scale cosmic microwave background (CMB) measure- ments and measurements of large-scale structure (galaxy surveys and the Lyforest). 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 Lyforest data to find the models best-fit cosmological parameters: h ¼ 0:71 þ0:04 � 0:03 , � bh 2 ¼ 0:0224 � 0:0009, � mh 2 ¼ 0:135 þ0:008 � 0:009 , � ¼ 0:17 � 0:06, ns(0.05 Mpc � 1 )=0 :93 � 0:03, and � 8 ¼ 0:84 � 0:04. WMAPs best determination of � ¼ 0:17 � 0:04 arises directly from the temperature- polarization (TE) data and not from this model fit, but they are consistent. These parameters imply that the age of the universe is 13:7 � 0:2 Gyr. With the Lyforest 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 � 0:02, and the equation of state of the dark energy, w < � 0:78 (95% confidence limit assuming w �� 1). 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 parameters — cosmology: observations — early universe On-line material: color figure

Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology

A simple cosmological model with only six parameters (matter density, � mh 2 , baryon density, � bh 2 , Hubble con- stant, H0, amplitude of fluctuations,� 8, optical depth,� , and a slope for the scalar perturbation spectrum, ns) fits not only the 3 year WMAP temperature and polarization data, but also small-scale CMB data, light element abundances, large-scalestructureobservations,andthesupernovaluminosity/distancerelationship.UsingWMAPdataonly,thebest- fit values for cosmological parameters for the power-law flatcold dark matter (� CDM) model are (� mh 2 ; � bh 2 ; h;ns;�;� 8) ¼(0:1277 þ0:0080 � 0:0079 ;0:02229 � 0:00073;0:732 þ0:031 � 0:032 ;0:958 � 0:016;0:089 � 0:030;0:761 þ0:049 � 0:048 ).The3year 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-Zeldovich-Peebles scale-invariant spectrum (ns ¼ 1; r ¼ 0). Adding additionaldatasetsimprovestheconstraintsonthesecomponentsandthespectralslope.Forpower-lawmodels,WMAP data alone puts an improved upper limit on the tensor-to-scalar ratio, r0:002 < 0:65 (95% CL) and the combination of WMAP and the lensing-normalized SDSS galaxy survey implies r0:002 < 0:30 (95% CL). Models that suppress large- scalepowerthrougharunningspectralindexoralarge-scalecutoffinthepowerspectrumareabetterfittotheWMAP and small-scale CMB data than the power-lawCDM model; however, the improvement in thefit to the WMAP data is only � � 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) datayieldsasignificantconstraintontheequationofstateofthedarkenergy,w ¼� 0:967 þ0:073 � 0:072 .Ifweassumew ¼� 1, then the deviations from the critical density, � K, are small: the combination of WMAP and the SNLS data implies � k ¼� 0:011 � 0:012. The combination of WMAP 3 year data plus the HST Key Project constraint on H0 implies � k ¼� 0:014 � 0:017 and � � ¼ 0:716 � 0:055. Even if we do not include the prior that the universe is flat, by com- biningWMAP,large-scalestructure,andsupernovadata,wecanstillputastrongconstraintonthedarkenergyequation of state, w ¼� 1:08 � 0:12. For a flat universe, the combination of WMAP and other astronomical data yield a con- straint on the sum of the neutrino masses, P m� <0:66 eV (95%CL). Consistent with the predictions of simple infla- tionary 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.

First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Preliminary maps and basic results

We present full-sky microwave maps in five frequency bands (23-94 GHz) from the Wilkinson Microwave Anisotropy Probe (WMAP) first-year sky survey. Calibration errors are less than 0.5%, and the low systematic error level is well specified. The cosmic microwave background (CMB) is separated from the foregrounds using multifrequency data. The sky maps are consistent with the 7° FWHM Cosmic Background Explorer (COBE) maps. We report more precise, but consistent, dipole and quadrupole values. The CMB anisotropy obeys Gaussian statistics with -58 < fNL < 134 (95% confidence level [CL]). The 2 ≤ l ≤ 900 anisotropy power spectrum is cosmic-variance-limited for l < 354, with a signal-to-noise ratio greater than 1 per mode to l = 658. The temperature-polarization cross-power spectrum reveals both acoustic features and a large-angle correlation from reionization. The optical depth of reionization is τ = 0.17 ± 0.04, which implies a reionization epoch of tr = 180 Myr (95% CL) after the big bang at a redshift of zr = 20 (95% CL) for a range of ionization scenarios. This early reionization is incompatible with the presence of a significant warm dark matter density.xa0xa0xa0xa0xa0A best-fit cosmological model to the CMB and other measures of large-scale structure works remarkably well with only a few parameters. The age of the best-fit universe is t0 = 13.7 ± 0.2 Gyr. Decoupling was tdec = 379 kyr after the big bang at a redshift of zdec = 1089 ± 1. The thickness of the decoupling surface was Δzdec = 195 ± 2. The matter density of the universe is Ωmh2 = 0.135, the baryon density is Ωbh2 = 0.0224 ± 0.0009, and the total mass-energy of the universe is Ωtot = 1.02 ± 0.02. It appears that there may be progressively less fluctuation power on smaller scales, from WMAP to fine-scale CMB measurements to galaxies and finally to the Lyα forest. This may be accounted for with a running spectral index of scalar fluctuations, fitted as ns = 0.93 ± 0.03 at wavenumber k0 = 0.05 Mpc-1 (leff ≈ 700), with a slope of dns/d ln k = -0.031 in the best-fit model. (For WMAP data alone, ns = 0.99 ± 0.04.) This flat universe model is composed of 4.4% baryons, 22% dark matter, and 73% dark energy. The dark energy equation of state is limited to w < -0.78 (95% CL). Inflation theory is supported with ns ≈ 1, Ωtot ≈ 1, Gaussian random phases of the CMB anisotropy, and superhorizon fluctuations implied by the temperature-polarization anticorrelations at decoupling. An admixture of isocurvature modes does not improve the fit. The tensor-to-scalar ratio is r(k0 = 0.002 Mpc-1) < 0.90 (95% CL). The lack of CMB fluctuation power on the largest angular scales reported by COBE and confirmed by WMAP is intriguing. WMAP continues to operate, so results will improve.

FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE * OBSERVATIONS: COSMOLOGICAL INTERPRETATION

The Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data provide stringent limits on deviations from the minimal, six-parameter Λxa0cold 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: Ω b h 2 = 0.02267+0.00058 –0.00059, Ω c h 2 = 0.1131 ± 0.0034, ΩΛ = 0.726 ± 0.015, ns = 0.960 ± 0.013, τ = 0.084 ± 0.016, and at k = 0.002 Mpc-1. From these, we derive σ8 = 0.812 ± 0.026, H 0 = 70.5 ± 1.3 km s-1 Mpc–1, Ω b = 0.0456 ± 0.0015, Ω c = 0.228 ± 0.013, Ω 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 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 < Ω 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 < Δα < 24 (95% CL) between the decoupling and the present epoch. We find the limit on the total mass of massive neutrinos of ∑m ν < 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.

Three year Wilkinson Microwave Anisotropy Probe (WMAP) observations: polarization analysis

The Wilkinson Microwave Anisotropy Probe (WMAP) has mapped the entire sky in five frequency bands between 23 and 94 GHz with polarization sensitive radiometers. We present three-year full-sky maps of the polarization and analyze them for foreground emission and cosmological implications. These observations open up a new window for understanding how the universe began and help set a foundation for future observations. WMAP observes significant levels of polarized foreground emission due to both Galactic synchrotron radiation and thermal dust emission. Synchrotron radiation is the dominant signal at l < 50 and ν . 40 GHz, while thermal dust emission is evident at 94 GHz. The least contaminated channel is at 61 GHz. We present a model of polarized foreground emission that captures the large angular scale characteristics of the microwave sky. After applying a Galactic mask that cuts 25.7% of the sky, we show that the high Galactic latitude rms polarized foreground emission, averaged over l = 4 − 6, ranges from ≈ 5 μK at 22 GHz to . 0.6 μK at 61 GHz. By comparison, the levels of intrinsic CMB polarization for a ΛCDM model with an optical depth of τ = 0.09 and assumed tensor to scalar ratio r = 0.3 are ≈ 0.3 μK for E-mode polarization and ≈ 0.03 μK for B-mode polarization. To analyze the maps for CMB polarization at l < 16, we subtract a model of the foreground emission. In the foreground corrected maps, we detect l(l+ 1)CEE l=<2−6>/2π = 0.086±0.029 (μK)2. This is interpreted as the result of rescattering of the CMB by free electrons released during reionization at zr = 10.9+2.7 −2.3 for a model with instantaneous reionization. By computing the likelihood of just the EE data as a function of τ we find τ = 0.10±0.03. When the same EE data are used in the full six parameter fit to all WMAP data (TT, TE, EE), we find τ = 0.09±0.03. We see no evidence for B-modes, limiting them to l(l+ 1)CBB l=<2−6>/2π = −0.04± 0.03 (μK)2. We perform a template fit to the E-mode and B-mode data with an approximate model for the tensor scalar ratio. We find that the limit from the polarization signals alone is r < 2.2 (95% CL) where r is evaluated at k = 0.002 Mpc−1. This corresponds to a limit on the cosmic density of gravitational waves of ΩGW h2 < 5×10−12. From the full WMAP analysis, we find r < 0.55 (95% CL) corresponding to a limit of ΩGW h2 < 1× 10−12 (95% CL). The limit on r is approaching the upper bound of predictions for some of the simplest models of inflation, r ∼ 0.3.

FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: LIKELIHOODS AND PARAMETERS FROM THE WMAP DATA

This paper focuses on cosmological constraints derived from analysis of WMAP data alone. A simple ?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: ? b h 2 = 0.02273 ? 0.00062, ? c h 2 = 0.1099 ? 0.0062, ?? = 0.742 ? 0.030, ns = 0.963+0.014 ?0.015, ? = 0.087 ? 0.017, and ?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, ?>0, at 5? significance. The redshift of an instantaneous reionization is constrained to be z reion = 11.0 ? 1.4 with 68% confidence. The 2? lower limit is z reion > 8.2, and the 3? limit is z reion > 6.7. This excludes a sudden reionization of the universe at z = 6 at more than 3.5? 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 ? ~ 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 ?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 ?m ? < 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.

Five-Year Wilkinson Microwave Anisotropy Probe Observations: Data Processing, Sky Maps, and Basic Results

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 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. Further scientific results from the five year data analysis are presented in six companion papers and are summarized in �7 of this paper.

SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP *) OBSERVATIONS: POWER SPECTRA AND WMAP-DERIVED PARAMETERS

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 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?. These new WMAP measurements provide important tests of big bang cosmology.

SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP ∗ ) OBSERVATIONS: SKY MAPS, SYSTEMATIC ERRORS, AND BASIC RESULTS

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 ?CDM 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 ? b h 2 = 0.02260 ? 0.00053, ? c h 2 = 0.1123 ? 0.0035, ?? = 0.728+0.015 ?0.016, ns = 0.963 ? 0.012, ? = 0.087 ? 0.014, and ?8 = 0.809 ? 0.024 (68% CL uncertainties). The temperature power spectrum signal-to-noise ratio per multipole is greater that unity for multipoles ? 919, allowing a robust measurement of the third acoustic peak. This measurement results in improved constraints on the matter density, ? 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? 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, ?m ? ? 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-Zeldovich-Peebles spectrum by >3?. These new WMAP measurements provide important tests of big bang cosmology.