Joanna Dunkley

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.

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

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.

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.

The Atacama Cosmology Telescope: Cosmological Parameters from the 2008 Power Spectrum

We present cosmological parameters derived from the angular power spectrum of the cosmic microwave background (CMB) radiation observed at 148?GHz and 218?GHz over 296?deg2 with the Atacama Cosmology Telescope (ACT) during its 2008 season. ACT measures fluctuations at scales 500 < ? < 10, 000. We fit a model for the lensed CMB, Sunyaev-Zeldovich (SZ), and foreground contribution to the 148?GHz and 218?GHz power spectra, including thermal and kinetic SZ, Poisson power from radio and infrared point sources, and clustered power from infrared point sources. At ? = 3000, about half the power at 148?GHz comes from primary CMB after masking bright radio sources. The power from thermal and kinetic SZ is estimated to be , where . The IR Poisson power at 148?GHz is (C ? = 5.5 ? 0.5 nK2), and a clustered IR component is required with , assuming an analytic model for its power spectrum shape. At 218?GHz only about 15% of the power, approximately 27 ?K2, is CMB anisotropy at ? = 3000. The remaining 85% is attributed to IR sources (approximately 50% Poisson and 35% clustered), with spectral index ? = 3.69 ? 0.14 for flux scaling as S(?)??. We estimate primary cosmological parameters from the less contaminated 148?GHz spectrum, marginalizing over SZ and source power. The ?CDM cosmological model is a good fit to the data (?2/dof = 29/46), and ?CDM parameters estimated from ACT+Wilkinson Microwave Anisotropy Probe (WMAP) are consistent with the seven-year WMAP limits, with scale invariant ns = 1 excluded at 99.7% confidence level (CL) (3?). A model with no CMB lensing is disfavored at 2.8?. By measuring the third to seventh acoustic peaks, and probing the Silk damping regime, the ACT data improve limits on cosmological parameters that affect the small-scale CMB power. The ACT data combined with WMAP give a 6? detection of primordial helium, with YP = 0.313 ? 0.044, and a 4? detection of relativistic species, assumed to be neutrinos, with N eff = 5.3 ? 1.3 (4.6 ? 0.8 with BAO+H 0 data). From the CMB alone the running of the spectral index is constrained to be dns /dln k = ?0.034 ? 0.018, the limit on the tensor-to-scalar ratio is r < 0.25 (95% CL), and the possible contribution of Nambu cosmic strings to the power spectrum is constrained to string tension G? < 1.6 ? 10?7 (95% CL).

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectra

We present the temperature and polarization angular power spectra of the cosmic microwave background (CMB) derived from the first 5 years of WMAP data. The 5-year temperature (TT) spectrum is cosmic variance limited up to multipole l=530, and individual l-modes have S/N>1 for l<920. The best fitting six-parameter LambdaCDM model has a reduced chi^2 for l=33-1000 of chi^2/nu=1.06, with a probability to exceed of 9.3%. There is now significantly improved data near the third peak which leads to improved cosmological constraints. The temperature-polarization correlation (TE) is seen with high significance. After accounting for foreground emission, the low-l reionization feature in the EE power spectrum is preferred by Deltachi^2=19.6 for optical depth tau=0.089 by the EE data alone, and is now largely cosmic variance limited for l=2-6. There is no evidence for cosmic signal in the BB, TB, or EB spectra after accounting for foreground emission. We find that, when averaged over l=2-6, l(l+1)C^{BB}_l/2pi < 0.15 uK^2 (95% CL).

THE ATACAMA COSMOLOGY TELESCOPE: SUNYAEV-ZEL'DOVICH-SELECTED GALAXY CLUSTERS AT 148 GHz IN THE 2008 SURVEY

We report on 23 clusters detected blindly as Sunyaev-ZELDOVICH (SZ) decrements in a 148 GHz, 455 deg2 map of the southern sky made with data from the Atacama Cosmology Telescope 2008 observing season. All SZ detections announced in this work have confirmed optical counterparts. Ten of the clusters are new discoveries. One newly discovered cluster, ACT-CL J0102–4915, with a redshift of 0.75 (photometric), has an SZ decrement comparable to the most massive systems at lower redshifts. Simulations of the cluster recovery method reproduce the sample purity measured by optical follow-up. In particular, for clusters detected with a signal-to-noise ratio greater than six, simulations are consistent with optical follow-up that demonstrated this subsample is 100% pure. The simulations further imply that the total sample is 80% complete for clusters with mass in excess of 6 × 1014 solar masses referenced to the cluster volume characterized by 500 times the critical density. The Compton y-X-ray luminosity mass comparison for the 11 best-detected clusters visually agrees with both self-similar and non-adiabatic, simulation-derived scaling laws.