M. R. Nolta

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.

NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: COSMOLOGICAL PARAMETER RESULTS

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 CDM 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, bh 2 , ch 2 , and , 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 5 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 CDM parameter space by a factor of 68,000 relative to pre-WMAP measurements. We investigate a number of data combinations and show that their CDM 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 k = 0.0027 +0.0039 0.0038 ; the summed mass of neutrinos is limited to P m < 0.44 eV (95% CL); and the number of relativistic species is found to lie within Ne = 3.84±0.40, when the full data are analyzed. The joint constraint on Ne and the primordial helium abundance, YHe, agrees with the prediction of standard Big Bang nucleosynthesis. We compare recent Planck measurements of the Sunyaev‐Zel’dovich eect 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. Subject headings: cosmic microwave background, cosmology: observations, early universe, dark matter, space vehicles, space vehicles: instruments, instrumentation: detectors, telescopes

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.

NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: FINAL MAPS AND RESULTS

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 CMB maps are presented. We now implement an optimal C ?1 weighting to compute the temperature angular power spectrum. The WMAP mission has resulted in a highly constrained ?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 eff = 3.84 ? 0.40). The model fit also implies that the age of the universe is t 0 = 13.772 ? 0.059 Gyr, and the fit Hubble constant is H 0 = 69.32 ? 0.80?km?s?1?Mpc?1. 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 (ns = 0.9608 ? 0.0080); and the universe is close to flat/Euclidean (). 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 ?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 ?CDM model and its precise and accurate parameters rooted in WMAP data stands as the standard model of cosmology.

Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Are There Cosmic Microwave Background Anomalies?

A simple six-parameter ?CDM 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 ?CDM 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 ?CDM model. We examine in detail the properties of the power spectrum data with respect to the ?CDM 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 ?CDM model, which is generally an acceptable statistical fit to WMAP and other cosmological data.

Three-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Beam Profiles, Data Processing, Radiometer Characterization, and Systematic Error Limits

The WMAP satellite has completed 3 years of observations of the cosmic microwave background radiation. The 3yeardataproductsincludeseveralsetsof fullskymapsoftheStokesI,Q,andUparametersinfivefrequencybands, spanning 23Y94 GHz, and supporting items such as beam window functions and noise covariance matrices. The processing used to produce the current sky maps and supporting products represents a significant advancement over the first-year analysis and is described herein. Improvements to the pointing reconstruction, radiometer gain modeling, window function determination, and radiometer spectral noise parameterization are presented. A detailed description of the updated data processing that produces maximum likelihood sky map estimates is presented, along withthemethodsusedtoproducereducedresolutionmapsandcorrespondingnoisecovariancematrices.Finally,two methods used to evaluate the noise of the full resolution sky maps are presented along with several representativeyear-to-yearnulltests,demonstratingthatskymapsproducedfromdatafromdifferentobservationalepochsare consistent. Subject headingg cosmic microwave background — instrumentation: detectors — space vehicles: instruments

Five-Year Wilkinson Microwave Anisotropy Probe Observations: Galactic Foreground Emission

We present a new estimate of foreground emission in the Wilkinson Microwave Anisotropy Probe (WMAP) data, using a Markov chain Monte Carlo method. The new technique delivers maps of each foreground component for a variety of foreground models with estimates of the uncertainty of each foreground component, and it provides an overall goodness-of-fit estimate. The resulting foreground maps are in broad agreement with those from previous techniques used both within the collaboration and by other authors. We find that for WMAP data, a simple model with power-law synchrotron, free-free, and thermal dust components fits 90% of the sky with a reduced χ2 ν of 1.14. However, the model does not work well inside the Galactic plane. The addition of either synchrotron steepening or a modified spinning dust model improves the fit. This component may account for up to 14% of the total flux at the Ka band (33 GHz). We find no evidence for foreground contamination of the cosmic microwave background temperature map in the 85% of the sky used for cosmological analysis.