Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results

TL;DR

The paper delivers the final nine-year WMAP cosmological parameter constraints, demonstrating that a six-parameter ΛCDM model remains an excellent fit when combined with external data such as high-$l$ CMB measurements, BAO, and $H_0$. It quantifies precise densities (Ωb h^2, Ωc h^2, ΩΛ), a 3% amplitude of primordial fluctuations, and a 5σ detection of primordial tilt, while constraining extensions like tensor modes, extra relativistic species, neutrino mass, curvature, and evolving dark energy. The analysis integrates updated likelihoods, external probes, and robust polarization tests, reinforcing the standard cosmological model and Big Bang nucleosynthesis predictions. The results also align with Planck SZ measurements and provide a strong foundation for future precision cosmology and inflationary theory testing.

Abstract

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.

Figures (11)

• Figure 1: A compilation of the CMB data used in the nine-year WMAP analysis. The WMAP data are shown in black, the extended CMB data set -- denoted 'eCMB' throughout -- includes SPT data in blue keisler/etal:2011, and ACT data in orange, das/etal:2011a. We also incorporate constraints from CMB lensing published by the SPT and ACT groups (not shown). The $\Lambda\mathrm{CDM}$ model fit to the WMAP data alone (shown in grey) successfully predicts the higher-resolution data.
• Figure 2: Two estimates of the WMAP nine-year power spectrum along with the best-fit model spectra obtained from each; black - the $C^{-1}$-weighted spectrum and best fit model; red - the same for the MASTER spectrum and model. The two spectrum estimates differ by up to 5% in the vicinity of $l \sim 50$ which mostly affects the determination of the spectral index, $n_s$, as shown in Table \ref{['tab:lcdm_wmap_79']}. We adopt the $C^{-1}$-weighted spectrum throughout the remainder of this paper.
• Figure 3: 68% and 95% CL regions for the $\Lambda\mathrm{CDM}$ parameters $n_s$, $10^9 \Delta_{\cal R}^2$, and $\Omega_bh^2$. There is a modest degeneracy between these three parameters in the six-parameter $\Lambda\mathrm{CDM}$ model, when fit to the nine-year WMAP data. The contours are derived from fits to the $C^{-1}$-weighted power spectrum, while the plus signs indicate the maximum likelihood point for the fit to the MASTER power spectrum. As shown in Figure \ref{['fig:Master_Cinv']}, the two model produce nearly identical spectra.
• Figure 4: Measurements of the scalar spectral index with CMB and BAO data. Left to right - contours of ($D_V(0.57)/r_s$,$n_s$), ($H_0$,$n_s$), ($\Omega_ch^2$,$n_s$). Black contours show constraints using WMAP nine-year data alone; blue contours include SPT and ACT data (WMAP+eCMB); red contours add the BAO prior(WMAP+eCMB+BAO). The BAO prior provides an independent measurement of the low-redshift distance, $D_v(z)/r_s,$ which maps to constraints on $\Omega_ch^2$ and $H_0$. When combined with CMB data, the joint constraints require a tilt in the primordial spectral index ($n_s$$<1$) at the 5$\sigma$ level.
• Figure 5: Measurements of $\Omega_ch^2$ and $H_0$ from CMB data only (blue contours, WMAP+eCMB), from CMB and BAO data (green contours, WMAP+eCMB+BAO), and from CMB and $H_0$ data (red contours, WMAP+eCMB+$H_0$). The two non-CMB priors push the constraints towards opposite ends of the range allowed by the CMB alone, but they are not inconsistent.