SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: POWER SPECTRA AND WMAP -DERIVED PARAMETERS

Abstract

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 < 919; and in band powers of width Δ l = 10, the signal-to-noise ratio exceeds unity up to l = 1060. The third acoustic peak in the TT spectrum is now well measured by WMAP . In the context of a flat ΛCDM model, this improvement allows us to place tighter constraints on the matter density from WMAP data alone, Ω m h 2 = 0.1334 +0.0056 −0.0055 , and on the epoch of matter-radiation equality, z eq = 3196 +134 −133 . The temperature-polarization (TE) spectrum is detected in the seven-year data with a significance of 20σ, compared to 13σ with the five-year data. We now detect the second dip in the TE spectrum near l ∼ 450 with high confidence. The TB and EB spectra remain consistent with zero, thus demonstrating low systematic errors and foreground residuals in the data. The low- l EE spectrum, a measure of the optical depth due to reionization, is detected at 5.5σ significance when averaged over l = 2–7: l ( l + 1) C EE l /(2π) = 0.074 +0.034 −0.025 μK 2 (68% CL). We now detect the high- l , 24 ⩽ l ⩽ 800, EE spectrum at over 8σ. The BB spectrum, an important probe of gravitational waves from inflation, remains consistent with zero; when averaged over l = 2–7, l ( l + 1) C BB l /(2π) < 0.055 μK 2 (95% CL). The upper limit on tensor modes from polarization data alone is a factor of two lower with the seven-year data than it was using the five-year data. The data remain consistent with the simple ΛCDM model: the best-fit TT spectrum has an effective χ 2 of 1227 for 1170 degrees of freedom, with a probability to exceed of 9.6%. The allowable volume in the six-dimensional space of ΛCDM parameters has been reduced by a factor of 1.5 relative to the five-year volume, while the ΛCDM model that allows for tensor modes and a running scalar spectral index has a factor of three lower volume when fit to the seven-year data. We test the parameter recovery process for bias and find that the scalar spectral index, n s , is biased high , but only by 0.09σ, while the remaining parameters are biased by <0.15σ. The improvement in the third peak measurement leads to tighter lower limits from WMAP on the number of relativistic degrees of freedom (e.g., neutrinos) in the early universe: N eff >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 >3σ. These new WMAP measurements provide important tests of big bang cosmology.