Three‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Polarization Analysis

Abstract

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 3 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 P 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 ¼ 4Y6, ranges from %5 K at 22 GHz to P0.6 K at 61 GHz. By comparison, the levels of intrinsic CMB polarization for a ÃCDM model with an optical depth of ¼ 0:09 and assumed tensor-to-scalar ratio r ¼ 0:3 are %0.3 K for E-mode polarization and %0.1 K for B-mode polarization. To analyze the maps for CMB polarization at l < 16, we subtract a model of the foreground emission that is based primarily on a scaling WMAP's 23 GHz map. In the foregroundcorrected maps, we detect l(l þ 1)C EE l¼ 2Y6 h i /2 ¼ 0:086 AE 0:029 (K) 2 . This is interpreted as the result of rescattering of the CMB by free electrons released during reionization at z r ¼ 10:9 þ2:7 À2:3 for a model with instantaneous reionization. By computing the likelihood of just the EE data as a function of we find ¼ 0:10 AE 0:03. When the same EE data are used in the full six-parameter fit to all WMAP data ( TT, TE, EE), we find ¼ 0:09 AE 0:03. Marginalization over the foreground subtraction affects this value by < 0:01. We see no evidence for B modes, limiting them to l(l þ 1)C BB l¼ 2Y6 h i /2 ¼ À0:04 AE 0:03 (K) 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 ¼ 0:002 Mpc À1 . This corresponds to a limit on the cosmic density of gravitational waves of GW h 2 < 5 ; 10 À12 . From the full WMAP analysis, we find r < 0:55 (95% CL) corresponding to a limit of GW h 2 < 1 ; 10 À12 (95% CL). The limit on r is approaching the upper bound of predictions for some of the simplest models of inflation, r $ 0:3. Subject headingg s: cosmic microwave background -cosmology: observations -polarization Online material: color figure

Gravitino dark matter and cosmological constraints

“…in a model with instantaneous reionization [67]. These new results replace the ones from the analysis of the first year WMAP data, in which τ = 0.17 ± 0.06 was interpreted to originate from reionization at z ∼ 20 [52].…”

“…These new results replace the ones from the analysis of the first year WMAP data, in which τ = 0.17 ± 0.06 was interpreted to originate from reionization at z ∼ 20 [52]. In the light of the polarization analysis of the three year WMAP observations [67], we do not list the (possibly overly restrictive) limit m WDM 10 keV, corresponding to (v rms,0 FS ) WDM 0.002 km/s, which was derived from the first year WMAP observations [68] and discussed in [27] for gravitinos from NLSP decays.…”

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

“…As can be seen in figure 34, both the mean likelihood and marginalised probability exhibits narrow peaks on particular frequencies only thereby leading to a discrete set of best fit submanifolds in the parameter space. From the WMAP team likelihood code [1,2,3,4], the best fit associated with the highest resonance peak leads to an overall χ 2 = 11239.9, which is a fit improvement of ∆χ 2 ≃ −12 with respect to the first order vanilla slow-roll model, for three additional parameters (see figure 35). Note that this value is larger that the one reported by the WMAP team [2], possibly due to the localisation of the highest likelihood resonance in a rather high frequency region log(ǫ 1 /σ 0 ) ≃ 170.…”

“…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 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.…”