Three‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Temperature Analysis

Abstract

We present new full-sky temperature maps in five frequency bands from 23 to 94 GHz, based on data from the first 3 years of the WMAP sky survey. The new maps are consistent with the first-year maps and are more sensitive. The 3 year maps incorporate several improvements in data processing made possible by the additional years of data and by a more complete analysis of the polarization signal. These include several new consistency tests as well as refinements in the gain calibration and beam response models. We employ two forms of multifrequency analysis to separate astrophysical foreground signals from the CMB, each of which improves on our first-year analyses. First, we form an improved ''Internal Linear Combination'' (ILC) map, based solely on WMAP data, by adding a bias-correction step and by quantifying residual uncertainties in the resulting map. Second, we fit and subtract new spatial templates that trace Galactic emission; in particular, we now use low-frequency WMAP data to trace synchrotron emission instead of the 408 MHz sky survey. The WMAP point source catalog is updated to include 115 new sources whose detection is made possible by the improved sky map sensitivity. We derive the angular power spectrum of the temperature anisotropy using a hybrid approach that combines a maximum likelihood estimate at low l (large angular scales) with a quadratic cross-power estimate for l > 30. The resulting multifrequency spectra are analyzed for residual point source contamination. At 94 GHz the unmasked sources contribute 128 AE 27 K 2 to l(l þ 1)C l /2 at l ¼ 1000. After subtracting this contribution, our best estimate of the CMB power spectrum is derived by averaging cross-power spectra from 153 statistically independent channel pairs. The combined spectrum is cosmic variance limited to l ¼ 400, and the signal-to-noise ratio per l-mode exceeds unity up to l ¼ 850. For bins of width Ál/l ¼ 3%, the signal-to-noise ratio exceeds unity up to l ¼ 1000. The first two acoustic peaks are seen at l ¼ 220:8 AE 0:7 and l ¼ 530:9 AE 3:8, respectively, while the first two troughs are seen at l ¼ 412:4 AE 1:9 and l ¼ 675:2 AE 11:1. The rise to the third peak is unambiguous; when the WMAP data are combined with higher resolution CMB measurements, the existence of a third acoustic peak is well established. Spergel et al. use the 3 year temperature and polarization data to constrain cosmological model parameters. A simple six-parameter ÃCDM model continues to fit CMB data and other measures of large-scale structure remarkably well. The new polarization data produce a better measurement of the optical depth to reionization, ¼ 0:089 AE 0:03. This new and tighter constraint on helps break a degeneracy with the scalar spectral index, which is now found to be n s ¼ 0:960 AE 0:016. If additional cosmological data sets are included in the analysis, the spectral index is found to be n s ¼ 0:947 AE 0:015.

Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

“…ǫ 1 and ǫ 2 ) and also at second order (i.e. the two previous ones plus ǫ 3 ). In subsections 3.3 to 3.6, we calculate the slow-roll parameters for the large field, small field, hybrid and running mass inflationary models.…”

“…Inflation stops when ǫ 1 = 1. Another way to express the acceleration of the scale factor is to combine equations (3). One gets a a = − 4π 3m 2…”

“…Following [52], we used a modified version of the CAMB code [10] to compute the CMB temperature and polarisation anisotropies seeded by the slow-roll scalar and tensor primordial power spectra of equation (45). The parameter space has been sampled by using Markov Chain Monte Carlo (MCMC) methods implemented in the COSMOMC code [11] and using the likelihood estimator provided by the WMAP team [2,4,3,1]. The likelihood code settings have been kept to their default values which include the pixel based analysis at large scales, a Gaussian likelihood for the beam, with diagonal covariance matrix, and point source corrections [3,53,6].…”

“…The parameter space has been sampled by using Markov Chain Monte Carlo (MCMC) methods implemented in the COSMOMC code [11] and using the likelihood estimator provided by the WMAP team [2,4,3,1]. The likelihood code settings have been kept to their default values which include the pixel based analysis at large scales, a Gaussian likelihood for the beam, with diagonal covariance matrix, and point source corrections [3,53,6]. We have also checked the sensitivity of our results to modifications of these options and no significant deviations has been observed.…”

“…The recent release of the three years WMAP data [1,2,3,4] constitutes an important step for the theory of inflation. One now has at our disposal high accuracy data that can be used to probe the details of the inflationary scenario and to learn about the physical conditions that prevailed in the very early universe, at very high energies comparable to the Grand Unified Theory (GUT) scale.…”