Five-year WMAP Research Articles

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 additional cosmological data sets. The WMAP data alone, and in combination, continue to be remarkably well fit by a six-parameter LCDM model. When WMAP data are combined with measurements of the high-l CMB anisotropy, the BAO scale, and the Hubble constant, the densities, Omegabh2, Omegach2, and Omega_L, 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 5sigma 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 LCDM parameter space by a factor of 68,000 relative to pre-WMAP measurements. We investigate a number of data combinations and show that their LCDM 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 -0.0027 (+0.0039/-0.0038); the summed mass of neutrinos is <0.44 eV (95% CL); and the number of relativistic species is found to be 3.84+/-0.40 when the full data are analyzed. The joint constraint on Neff and the primordial helium abundance 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.

Constraints on primordial gravitational waves with variable sound speed from current CMB data

We make a comprehensive investigation of the observational effect of the inflation consistency relation. We focus on the general single-field inflation model with the consistency relation $r=-8c_s n_t$, and investigate the observational constraints of sound speed $c_s$ by using the Seven-Year WMAP data, the BICEP tensor power spectrum data, and the constraints on $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ from the Five-Year WMAP observations. We find that the constraints on the tensor-to-scalar ratio $r$ is much tighter if $c_s$ is small, since a large tilt $n_t$ is strongly constrained by the observations. We obtain $r<0.37, 0.27$ and 0.09 ($dn_s/d\ln k=0$) for $c_s$=1, 0.1 and 0.01 models at 95.4% confidence level. When taking smaller values of $c_s$, the positive correlation between $r$ and $n_s$ also leads to slightly tighter constraint on the upper bound of $n_s$, while the running of scalar spectral index $dn_s/d\ln k$ is generally unaffected. For the sound speed $c_s$, it is not well constrained if only the CMB power spectrum data is used, while the constraints are obtainable by taking $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ priors into account. With the constraining data of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$, we find that, $c_s\lesssim 0.01$ region is excluded at 99.7% CL, and the $c_s=1$ case (the single-field slow-roll inflation) is slightly disfavored at 68.3% CL. In addition, the inclusion of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ into the analysis can improve the constraints on $r$ and $n_s$. We further discuss the implications of our constraints on the test of inflation models.

Anomalous variance in the WMAP data and Galactic foreground residuals

A previous work (Monteser\'in et al. 2008) estimated the CMB variance from the three-year WMAP data, finding a lower value than expected from Gaussian simulations using the WMAP best-fit cosmological model. We repeat the analysis on the five-year WMAP data using a new estimator with lower bias and variance. Our results confirm this anomaly at higher significance, namely with a p-value of 0.31%. We perform the analysis using different exclusion masks, showing that a particular region of the sky near the Galactic plane shows a higher variance than 95.58% of the simulations whereas the rest of the sky has a lower variance than 99.96% of the simulations. The relative difference in variance between both regions is bigger than in 99.64% of the simulations. This anisotropic distribution of power seems to be causing the anomaly since the model assumes isotropy. Furthermore, this region has a clear frequency dependence between 41GHz and 61GHz or 94GHz suggesting that Galactic foreground residuals could be responsible for the anomaly. Moreover, removing the quadrupole and the octopole from data and simulations the anomaly disappears. The variance anomaly and the previously reported quadrupole and octopole alignment seem therefore to be related and could have a common origin. We discuss different possible causes and Galactic foreground residuals seem to be the most likely one. These residuals would affect the estimation of the angular power spectrum from the WMAP data, which is used to generate Gaussian simulations, giving rise to an inconsistency between the estimated and expected CMB variance. If the presence of residuals is confirmed, the estimation of the cosmological parameters could be affected.

CMB constraints on non-commutative geometry during inflation

We investigate the primordial power spectrum of the density perturbations based on the assumption that spacetime is noncommutative in the early stage of inflation. Due to the spacetime noncommutativity, the primordial power spectrum can lose rotational invariance. Using the k-inflation model and slow-roll approximation, we show that the deviation from rotational invariance of the primordial power spectrum depends on the size of noncommutative length scale L_s but not on sound speed. We constrain the contributions from the spacetime noncommutativity to the covariance matrix for the harmonic coefficients of the CMB anisotropies using five-year WMAP CMB maps. We find that the upper bound for L_s depends on the product of sound speed and slow-roll parameter. Estimating this product using cosmological parameters from the five-year WMAP results, the upper bound for L_s is estimated to be less than 10^{-27} cm at 99.7% confidence level.

NON-GAUSSIANITIES IN THE LOCAL CURVATURE OF THE FIVE-YEAR WMAP DATA

ABSTRACT Using the five-year WMAP data, we re-investigate claims of non-Gaussianities and asymmetries detected in local curvature statistics of the one-year WMAP data. In Hansen et al., it was found that the northern ecliptic hemisphere was non-Gaussian at the ∼1% level testing the densities of hill, lake, and saddle points based on the second derivatives of the cosmic microwave background temperature map. The five-year WMAP data have a much lower noise level and better control of systematics. Using these, we find that the anomalies are still present at a consistent level. Also the direction of maximum non-Gaussianity remains. Due to limited availability of computer resources, Hansen et al. were unable to calculate the full covariance matrix for the χ2-test used. Here, we apply the full covariance matrix instead of the diagonal approximation and find that the non-Gaussianities disappear and there is no preferred non-Gaussian direction. We compare with simulations of weak lensing to see if this may cause the observed non-Gaussianity when using a diagonal covariance matrix. We conclude that weak lensing does not produce non-Gaussianity in the local curvature statistics at the scales investigated in this paper. The cause of the non-Gaussian detection in the case of a diagonal matrix remains unclear.

Inflationary scenario in the supersymmetric economical 3-3-1 model

We construct the supersymmetric economical 3-3-1 model which contains inflationary scenario and avoids the monopole puzzle. Based on the spontaneous symmetry breaking pattern (with three steps), the $F$-term inflation is derived. The slow-roll parameters $\ep$ and $\eta$ are calculated. By imposing as experimental five-year WMAP data on the spectral index $n$, we have derived a constraint on the number of e-folding $N_Q$ to be in the range from 25 to 50. The scenario for large-scale structure formation implied by the model is a mixed scenario for inflation and cosmic string, and the contribution to the CMBR temperature anisotropy depends on the ratio $\frac{M_X}{M_P}$. From the COBE data, we have obtained the constraint on the $M_X$ to be $M_X\in[1.22 \times 10^{16} - 0.98 \times 10^{17}]$ GeV. The upper value $M_X\simeq 10^{17}$ GeV is a result of the analysis in which the inflationary contribution to the temperature fluctuations measured by the COBE is 90%. The coupling $\alpha$ varies in the range: $ 10^{-7} - 10^{-1} $. This value is not so small, and it is a common characteristics of the supersymmetric unified models with the inflationary scenario. The spectral index $n$ is a little bit smaller than 0.98. The SUGRA corrections are slightly different from the previous consideration. When $\xi \ll 1$ and $ \al $ lies in the above range, the spectral index gets the value consistent with the experimental five-year WMAP data. Comparing with string theory, one gets $\xi < 10^{-8}$. Numerical analysis shows that $ \al \approx 10^{-6}$. To get inflation contribution to the CMBR temperature anisotropy $\approx 90%$, the mass scale $M_X \sim 3.5 \times 10^{14}$ GeV.

Non-Gaussianity in the foreground-reduced CMB maps

[Abridged]: A detection or nondetection of primordial non-Gaussianity by using the CMB data is crucial not only to discriminate inflationary models but also to test alternative scenarios. Non-Gaussianity offers, therefore, a powerful probe of the physics of the primordial universe. The extraction of primordial non-Gaussianity is a difficult enterprise since several effects of non-primordial nature can produce non-Gaussianity. Most of the Gaussianity analyses of CMB data have been performed by using part-sky frequency, where masks are used to deal with the galactic diffuse foreground emission. However, full-sky map seems to be potentially more appropriate to test for Gaussianity of the CMB data. On the other hand, masks can induce bias in some non-Gaussianity analyses. Here we use two recent large-angle non-Gaussianity indicators, based on skewness and kurtosis of large-angle patches of CMB maps, to examine the question of non-Gaussianity in the available full-sky five-year and seven-year WMAP maps. We show that these full-sky foreground-reduced maps present a significant deviation from Gaussianity of different levels, which vary with the foreground-reducing procedures. We also make a Gaussianity analysis of the foreground-reduced five-year and seven-year WMAP maps with a KQ75 mask, and compare with the similar analysis performed with the full-sky foreground-reduced maps. This comparison shows a significant reduction in the levels of non-Gaussianity when the mask is employed, which provides indications on the suitability of the foreground-reduced maps as Gaussian reconstructions of the full-sky CMB.

THE TWO- AND THREE-POINT CORRELATION FUNCTIONS OF THE POLARIZED FIVE-YEARWMAPSKY MAPS

We present the two- and three-point real space correlation functions of the five-year WMAP sky maps, and compare the observed functions to simulated LCDM concordance model ensembles. In agreement with previously published results, we find that the temperature correlation functions are consistent with expectations. However, the pure polarization correlation functions are acceptable only for the 33GHz band map; the 41, 61, and 94 GHz band correlation functions all exhibit significant large-scale excess structures. Further, these excess structures very closely match the correlation functions of the two (synchrotron and dust) foreground templates used to correct the WMAP data for galactic contamination, with a cross-correlation statistically significant at the 2sigma-3sigma confidence level. The correlation is slightly stronger with respect to the thermal dust template than with the synchrotron template.

GEOMETRICAL DIAGNOSTIC FOR THE GENERALIZED CHAPLYGIN GAS MODEL

A new diagnostic method, Om, is applied to the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy. On the basis of the recently observed data — the Union supernovae, the observational Hubble data, the SDSS baryon acoustic peak and the five-year WMAP shift parameter — we show the discriminations between the GCG model and the ΛCDM model. Furthermore, it is calculated that the current equation of state of dark energy w 0de = -0.964, according to the GCG model.

Observational constraint on generalized Chaplygin gas model

We investigate observational constraints on the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy from the latest observational data: the Union SNe Ia data, the observational Hubble data, the SDSS baryon acoustic peak and the five-year WMAP shift parameter. It is obtained that the best fit values of the GCG model parameters with their confidence level are $A_{s}=0.73^{+0.06}_{-0.06}$ ($1\sigma$) $^{+0.09}_{-0.09}$ $(2\sigma)$, $\alpha=-0.09^{+0.15}_{-0.12}$ ($1\sigma$) $^{+0.26}_{-0.19}$ $(2\sigma)$. Furthermore in this model, we can see that the evolution of equation of state (EOS) for dark energy is similar to quiessence, and its current best-fit value is $w_{0de}=-0.96$ with the $1\sigma$ confidence level $-0.91\geq w_{0de}\geq-1.00$.

FIVE-YEARWILKINSON MICROWAVE ANISOTROPY PROBE(WMAP) OBSERVATIONS: BAYESIAN ESTIMATION OF COSMIC MICROWAVE BACKGROUND POLARIZATION MAPS

We describe a sampling method to estimate the polarized CMB signal from observed maps of the sky. We use a Metropolis-within-Gibbs algorithm to estimate the polarized CMB map, containing Q and U Stokes parameters at each pixel, and its covariance matrix. These can be used as inputs for cosmological analyses. The polarized sky signal is parameterized as the sum of three components: CMB, synchrotron emission, and thermal dust emission. The polarized Galactic components are modeled with spatially varying power law spectral indices for the synchrotron, and a fixed power law for the dust, and their component maps are estimated as by-products. We apply the method to simulated low resolution maps with pixels of side 7.2 degrees, using diagonal and full noise realizations drawn from the WMAP noise matrices. The CMB maps are recovered with goodness of fit consistent with errors. Computing the likelihood of the E-mode power in the maps as a function of optical depth to reionization, tau, for fixed temperature anisotropy power, we recover tau=0.091+-0.019 for a simulation with input tau=0.1, and mean tau=0.098 averaged over 10 simulations. A `null' simulation with no polarized CMB signal has maximum likelihood consistent with tau=0. The method is applied to the five-year WMAP data, using the K, Ka, Q and V channels. We find tau=0.090+-0.019, compared to tau=0.086+-0.016 from the template-cleaned maps used in the primary WMAP analysis. The synchrotron spectral index, beta, averaged over high signal-to-noise pixels with standard deviation sigma(beta)<0.25, but excluding ~6% of the sky masked in the Galactic plane, is -3.03+-0.04. This estimate does not vary significantly with Galactic latitude, although includes an informative prior.

Revising the Predictions of Inflation for the Cosmic Microwave Background Anisotropies

We point out that, if quantum field renormalization is taken into account and the counterterms are evaluated at the Hubble-radius crossing time or few e-foldings after it, the predictions of slow-roll inflation for both the scalar and the tensorial power spectrum change significantly. This leads to a change in the consistency condition that relates the tensor-to-scalar amplitude ratio with spectral indices. A reexamination of the potentials varphi;{2} and varphi;{4} shows that both are compatible with five-year WMAP data. Only when the counterterms are evaluated at much larger times beyond the end of inflation does one recover the standard predictions. The alternative predictions presented here may soon come within the range of measurement of near-future experiments.

COSMOLOGICAL PARAMETERS FROM THE QUAD CMB POLARIZATION EXPERIMENT

In this paper, we present a parameter estimation analysis of the polarization and temperature power spectra from the second and third season of observations with the QUaD experiment. QUaD has for the first time detected multiple acoustic peaks in the E-mode polarization spectrum with high significance. Although QUaD-only parameter constraints are not competitive with previous results for the standard six-parameter ΛCDM cosmology, they do allow meaningful polarization-only parameter analyses for the first time. In a standard six-parameter ΛCDM analysis, we find the QUaD TT power spectrum to be in good agreement with previous results. However, the QUaD polarization data show some tension with ΛCDM. The origin of this 1σ-2σ tension remains unclear, and may point to new physics, residual systematics, or simple random chance. We also combine QUaD with the five-year WMAP data set and the SDSS luminous red galaxies 4th data release power spectrum, and extend our analysis to constrain individual isocurvature mode fractions, constraining cold dark matter density, αcdmi < 0.11 (95% confidence limit (CL)), neutrino density, αndi < 0.26 (95% CL), and neutrino velocity, αnvi < 0.23 (95% CL), modes. Our analysis sets a benchmark for future polarization experiments.

Searching for non-Gaussianity in the WMAP data

Some analyses of recent cosmic microwave background (CMB) data have provided hints that there are deviations from Gaussianity in the WMAP CMB temperature fluctuations. Given the far-reaching consequences of such a non-Gaussianity for our understanding of the physics of the early universe, it is important to employ alternative indicators in order to determine whether the reported non-Gaussianity is of cosmological origin, and/or extract further information that may be helpful for identifying its causes. We propose two new non-Gaussianity indicators, based on skewness and kurtosis of large-angle patches of CMB maps, which provide a measure of departure from Gaussianity on large angular scales. A distinctive feature of these indicators is that they provide sky maps of non-Gaussianity of the CMB temperature data, thus allowing a possible additional window into their origins. Using these indicators, we find no significant deviation from Gaussianity in the three and five-year WMAP Internal Linear Combination (ILC) map with KQ75 mask, while the ILC unmasked map exhibits deviation from Gaussianity, quantifying therefore the WMAP team recommendation to employ the new mask KQ75 for tests of Gaussianity. We also use our indicators to test for Gaussianity the single frequency foreground unremoved WMAP three and five-year maps, and show that the K and Ka maps exhibit a clear indication of deviation from Gaussianity even with the KQ75 mask. We show that our findings are robust with respect to the details of the method.

EXTRAGALACTIC POINT SOURCE SEARCH IN FIVE-YEARWMAP41, 61, AND 94 GHz MAPS

We present the results of an extragalactic point source search using the five-year WMAP 41, 61 and 94 GHz (Q-, V- and W-band) temperature maps. This work is an extension of our point source search in the WMAP maps applying a CMB-free technique. An internal linear combination (ILC) map has been formed from the three-band maps, with the weights chosen to remove the CMB anisotropy signal as well as to favor a selection of flat-spectrum sources. We find 381 sources at the > 5 sigma level outside the WMAP point source detection mask in the ILC map, among which 89 are "new" (i.e., not present in the WMAP catalog). Source fluxes have been calculated and corrected for the Eddington bias. We have solidly identified 367 (96.3%) of our sources. The 1 sigma positional uncertainty is estimated to be 2'. The 14 unidentified sources could be either extended radio structure or obscured by Galactic emission. We have also applied the same detection process on simulated maps and found 364+/-21 detections on average. The recovered source distribution N(>S) agrees well with the simulation input, which proves the reliability of this method.

Reconstruction of the primordial fluctuation spectrum from the five-year WMAP data by the cosmic inversion method with band-power decorrelation analysis

The primordial curvature fluctuation spectrum is reconstructed by the cosmic inversion method using the five-year Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background temperature anisotropy. We apply the covariance matrix analysis and decompose the reconstructed spectrum into statistically independent band-powers. The statistically significant deviation from a simple power-law spectrum suggested by the analysis of the first-year data is not found in the five-year data except possibly at one point near the border of the wave number domain where accurate reconstruction is possible.

Poincaré dodecahedral space parameter estimates

We aim to improve the surface of last scattering (SLS) optimal cross-correlation method in order to refine estimates of the Poincar\'e dodecahedral space (PDS) cosmological parameters. We analytically derive the formulae required to exclude points on the sky that cannot be members of close SLS-SLS cross-pairs. These enable more efficient pair selection without sacrificing uniformity of the underlying selection process. In certain cases this decreases the calculation time and increases the number of pairs per separation bin. (i) We recalculate Monte Carlo Markov Chains (MCMC) on the five-year WMAP data; and (ii) we seek PDS solutions in a small number of Gaussian random fluctuation (GRF) simulations. For 5 < alpha/deg < 60, a calculation speed-up of 3-10 is obtained. (i) The best estimates of the PDS parameters for the five-year WMAP data are similar to those for the three-year data. (ii) Comparison of the optimal solutions found by the MCMC chains in the observational map to those found in the simulated maps yields a slightly stronger rejection of the simply connected model using $\alpha$ than using the twist angle $\phi$. The best estimate of $\alpha$ implies that_given a large scale auto-correlation as weak as that observed,_ the PDS-like cross-correlation signal in the WMAP data is expected with a probability of less than about 10%. The expected distribution of $\phi$ from the GRF simulations is approximately Gaussian around zero, it is not uniform on $[-\pi,\pi]$. We infer that for an infinite, flat, cosmic concordance model with Gaussian random fluctuations, the chance of finding_both_ (a) a large scale auto-correlation as weak as that observed,_and_ (b) a PDS-like signal similar to that observed is less than about 0.015% to 1.25%.