Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters

TL;DR

The paper delivers the WMAP 7-year angular power spectra and uses them to constrain cosmology with a focus on a flat ΛCDM model, while testing extensions such as tensors, running, isocurvature modes, curvature, and varying neutrino content. It introduces methodological advances in map-making and likelihood evaluation, performs extensive bias and goodness-of-fit tests, and reports improved constraints on key parameters (e.g., $\Omega_b h^2$, $\Omega_c h^2$, $n_s$, $\tau$, $N_{\rm eff}$, $\sum m_\nu$). The findings reinforce the ΛCDM paradigm, tighten limits on new physics like primordial gravitational waves, and provide high-precision measurements of reionization history and helium abundance, with implications for early-universe physics and neutrino cosmology.

Abstract

(Abridged) We present the angular power spectra derived from the 7-year maps and discuss the cosmological conclusions that can be inferred from WMAP data alone. The third acoustic peak in the TT spectrum is now well measured by WMAP. In the context of a flat LambdaCDM model, this improvement allows us to place tighter constraints on the matter density from WMAP data alone, and on the epoch of matter-radiation equality, The temperature-polarization (TE) spectrum is detected in the 7-year data with a significance of 20 sigma, compared to 13 sigma with the 5-year data. The low-l EE spectrum, a measure of the optical depth due to reionization, is detected at 5.5 sigma significance when averaged over l = 2-7. The BB spectrum, an important probe of gravitational waves from inflation, remains consistent with zero. The upper limit on tensor modes from polarization data alone is a factor of 2 lower with the 7-year data than it was using the 5-year data (Komatsu et al. 2010). We test the parameter recovery process for bias and find that the scalar spectral index, ns, is biased high, but only by 0.09 sigma, while the remaining parameters are biased by < 0.15 sigma. 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: Neff > 2.7 (95% CL). Also, using WMAP data alone, the primordial helium mass fraction is found to be YHe = 0.28+0.14-0.15, and with data from higher-resolution CMB experiments included, we now establish the existence of pre-stellar helium at > 3 sigma (Komatsu et al. 2010).

Figures (14)

• Figure 1: The 7-year temperature (TT) power spectrum from WMAP. The third acoustic peak and the onset of the Silk damping tail are now well measured by WMAP. The curve is the $\Lambda\mathrm{CDM}$ model best fit to the 7-year WMAP data: $\Omega_bh^2$$=0.02270$, $\Omega_ch^2$$=0.1107$, $\Omega_\Lambda$$=0.738$, $\tau$$=0.086$, $n_s$$=0.969$, $\Delta_{\cal R}^2$$=2.38\times10^{-9}$, and $A_{\rm SZ}$$=0.52$. The plotted errors include instrument noise, but not the small, correlated contribution due to beam and point source subtraction uncertainty. The gray band represents cosmic variance. A complete error treatment is incorporated in the WMAP likelihood code. The points are binned in progressively larger multipole bins with increasing $l$; the bin ranges are included in the 7-year data release.
• Figure 2: The high-$l$ TT spectrum measured by WMAP, showing the improvement with 7 years of data. The points with errors use the full data set while the boxes show the 5-year results with the same binning. The TT measurement is improved by $>$30% in the vicinity of the third acoustic peak (at $l \approx 800$), while the 2 bins from $l$ = 1000--1200 are new with the 7-year data analysis.
• Figure 3: The 7-year temperature-polarization (TE) cross-power spectrum measured by WMAP. The second trough (TE$<$0) in the spectrum in the vicinity of $l=450$ is now clearly detected. The green curve is the $\Lambda\mathrm{CDM}$ model best fit to the 7-year WMAP data, as in Figure \ref{['figure_tt']}. The plotted errors depict the diagonal elements of the covariance matrix and include both cosmic variance and instrument noise. A complete error treatment is incorporated in the WMAP likelihood code. Note that the plotted spectrum is $(l+1)C^{\rm TE}_l/(2\pi)$, and not $l(l+1)C^{\rm TE}_l/(2\pi)$.
• Figure 4: The TE and TB high-$l$ spectra measured by WMAP, showing the improvement with 7 years of data. The points with errors use the full data set while the boxes show the 5-year results with the same binning. The spectra are greatly improved by the addition of W-band data. The non-detection of TB signal is expected; it provides a good check of systematic errors and foreground residuals, and can be also used to set limits on polarization rotation due to parity-violating effects (§\ref{['sec_tp_spec']} and komatsu/etal:prep).
• Figure 5: The 7-year temperature-polarization (TB) cross-power spectrum measured by WMAP. This spectrum is predicted to be zero in the basic $\Lambda\mathrm{CDM}$ model and the measured spectrum is consistent with zero. TB provides a useful null test for systematic errors and foreground residuals. komatsu/etal:prep use the TB and TE spectra to place an upper limit on polarization rotation due to parity-violating effects. The TB $\chi^2$ for the null hypothesis (TB=0) is 793.5 for 777 degrees of freedom. The probability to exceed that amount is 33%. Note that the plotted spectrum is $(l+1)C^{\rm TB}_l/(2\pi)$, and not $l(l+1)C^{\rm TB}_l/(2\pi)$.