Five-Year Wilkinson Microwave Anisotropy Probe Observations: Likelihoods and Parameters from the WMAP Data

This paper focuses on cosmological constraints derived from analysis of WMAP data alone. A simple ΛCDM 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: Ω _b h ² = 0.02273 ± 0.00062, Ω _c h ² = 0.1099 ± 0.0062, Ω_Λ = 0.742 ± 0.030, n_s = 0.963^+0.014 _-0.015, τ = 0.087 ± 0.017, and σ₈ = 0.796 ± 0.036, with h = 0.719^+0.026 _-0.027. With five years of polarization data, we have measured the optical depth to reionization, τ>0, at 5σ significance. The redshift of an instantaneous reionization is constrained to be z _reion = 11.0 ± 1.4 with 68% confidence. The 2σ lower limit is z _reion > 8.2, and the 3σ limit is z _reion > 6.7. This excludes a sudden reionization of the universe at z = 6 at more than 3.5σ 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 the foreground treatment of τ ~ 0.01. This cosmological model also fits small-scale cosmic microwave background (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 nonzero cosmic neutrino background, or a background of relativistic species, with the standard three light neutrino species preferred over the best-fit ΛCDM model with N _eff = 0 at >99.5% confidence, and N _eff > 2.3(95%confidence limit (CL)) when varied. The five-year WMAP data improve the upper limit on the tensor-to-scalar ratio, r < 0.43(95%CL), for power-law models, and halve the limit on r for models with a running index, r < 0.58(95%CL). With longer integration we find no evidence for a running spectral index, with dn_s /dln k = -0.037 ± 0.028, and find improved limits on isocurvature fluctuations. The current WMAP-only limit on the sum of the neutrino masses is ∑m _ν < 1.3 eV(95%CL), which is robust, to within 10%, to a varying tensor amplitude, running spectral index, or dark energy equation of state.

WMAP is the result of a partnership between Princeton University and NASA's Goddard Space Flight Center. Scientific guidance is provided by the WMAP Science Team.