Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data

TL;DR

This study analyzes the five-year WMAP data to constrain a flat ΛCDM cosmology using temperature and polarization measurements, achieving a high-significance detection of reionization and tighter limits on fundamental parameters. It demonstrates consistency with external data sets (BAO, SN Ia, H0, weak lensing) and places new evidence for light relativistic species (N_eff ≈ 3) and a nonzero neutrino background, while pushing limits on tensor modes and running of the spectral index. The paper also develops robust methods for foreground treatment and low-ℓ likelihoods, including alternative polarization-cleaning approaches, and assesses extended cosmologies with varying neutrino properties, curvature, and dark-energy equation of state. Overall, WMAP5 strengthens the standard ΛCDM picture, highlights neutrino physics imprints on the CMB, and provides a solid foundation for incorporating higher-precision data from Planck.

Abstract

This paper focuses on cosmological constraints derived from analysis of WMAP data alone. A simple LCDM cosmological model fits the five-year WMAP temperature and polarization data. The basic parameters of the model are consistent with the three-year data and now better constrained: Omega_b h^2 = 0.02273+-0.00062, Omega_c h^2 = 0.1099+-0.0062, Omega_L = 0.742+-0.030, n_s = 0.963+0.014- 0.015, tau = 0.087+-0.017, sigma_8 = 0.796+-0.036. With five years of polarization data, we have measured the optical depth to reionization, tau>0, at 5 sigma significance. The redshift of an instantaneous reionization is constrained to be z_reion = 11.0+-1.4 with 68% confidence. This excludes a sudden reionization of the universe at z=6 at more than 3.5 sigma significance, suggesting that reionization was an extended process. Using two methods for polarized foreground cleaning we get consistent estimates for the optical depth, indicating an error due to foreground treatment of tau~0.01. This cosmological model also fits small-scale CMB data, and a range of astronomical data measuring the expansion rate and clustering of matter in the universe. We find evidence for the first time in the CMB power spectrum for a non-zero cosmic neutrino background, or a background of relativistic species, with the standard three light neutrino species preferred over the best-fit LCDM model with N_eff=0 at >99.5% confidence, and N_eff > 2.3 (95% CL) when varied. The five-year WMAP data improve the upper limit on the tensor-to-scalar ratio to r < 0.43 (95% CL), for power-law models. With longer integration we find no evidence for a running spectral index, with dn_s/dlnk = -0.037+-0.028.

Figures (18)

• Figure 1: This figure compares the low-$\ell$ TT power spectrum computed with two different techniques. At each $\ell$ value, we plot the maximum likelihood value (tic mark), the region where the likelihood is greater than 50% of the peak value (thick line) and the region where the likelihood is greater than 95% of the peak value (thin line). The black lines (left side of each pair) are estimated by Gibbs sampling using the ILC map smoothed with a 5 degree Gaussian beam (at HEALPIX $N_{\rm side} = 32$). The light blue line (right side of the pair) is estimated with a pixel-based likelihood code with $N_{\rm side} = 16$. The slight differences between the points are primarily due to differences in resolution. At each multipole, the likelihood is sampled by fixing the other $C_{\ell}$ values at a fiducial spectrum (red).
• Figure 2: The temperature angular power spectrum corresponding to the WMAP-only best-fit $\Lambda$CDM model. The grey dots are the unbinned data; the black data points are binned data with 1$\sigma$ error bars including both noise and cosmic variance computed for the best-fit model.
• Figure 3: Constraints on $\Lambda$CDM parameters from the five-year WMAP data. The two-dimensional 68% and 95% marginalized limits are shown in blue. They are consistent with the three-year constraints (grey). Tighter limits on the amplitude of matter fluctuations, $\sigma_8$, and the cold dark matter density $\Omega_c h^2$, arise from a better measurement of the third temperature (TT) acoustic peak. The improved measurement of the EE spectrum provides a 5$\sigma$ detection of the optical depth to reionization, $\tau$, which is now almost uncorrelated with the spectral index $n_s$.
• Figure 4: Constraints from the five-year WMAP data on $\Lambda$CDM parameters (blue), showing marginalized one-dimensional distributions and two-dimensional 68% and 95% limits. Parameters are consistent with the three-year limits (grey) from spergel/etal:2007, and are now better constrained.
• Figure 5: Left: Marginalized probability distribution for $z_{\rm reion}$ in the standard model with instantaneous reionization. Sudden reionization at $z=6$ is ruled out at 3.5$\sigma$, suggesting that reionization was a gradual process. Right: In a model with two steps of reionization (with ionization fraction $x_e$ at redshift $z_r$, followed by full ionization at $z=7$), the WMAP data are consistent with an extended reionization process.