Three‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Implications for Cosmology

Abstract

A simple cosmological model with only six parameters (matter density, Ω m h 2 , baryon density, Ω b h 2 , Hubble constant, H 0 , amplitude of fluctuations, σ 8 , optical depth, τ, and a slope for the scalar perturbation spectrum, n s ) fits not only the 3 year WMAP temperature and polarization data, but also small-scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the best-fit values for cosmological parameters for the power-law flat Λ cold dark matter (ΛCDM) model are (Ω m h 2 ,Ω b h 2 , h , n s ,τ,σ 8 ) = (0.1277 ,0.02229 ± 0.00073,0.732 ,0.958 ± 0.016,0.089 ± 0.030,0.761 ). The 3 year data dramatically shrink the allowed volume in this six-dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power-law spectrum, the WMAP data alone require dark matter and favor a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum ( n s = 1, r = 0). Adding additional data sets improves the constraints on these components and the spectral slope. For power-law models, WMAP data alone puts an improved upper limit on the tensor-to-scalar ratio, r 0.002 < 0.65 (95% CL) and the combination of WMAP and the lensing-normalized SDSS galaxy survey implies r 0.002 < 0.30 (95% CL). Models that suppress large-scale power through a running spectral index or a large-scale cutoff in the power spectrum are a better fit to the WMAP and small-scale CMB data than the power-law ΛCDM model; however, the improvement in the fit to the WMAP data is only Δχ 2 = 3 for 1 extra degree of freedom. Models with a running-spectral index are consistent with a higher amplitude of gravity waves. In a flat universe, the combination of WMAP and the Supernova Legacy Survey (SNLS) data yields a significant constraint on the equation of state of the dark energy, w = -0.967 . If we assume w = -1, then the deviations from the critical density, Ω K , are small: the combination of WMAP and the SNLS data implies Ω k = -0.011 ± 0.012. The combination of WMAP 3 year data plus the HST Key Project constraint on H 0 implies Ω k = -0.014 ± 0.017 and Ω Λ = 0.716 ± 0.055. Even if we do not include the prior that the universe is flat, by combining WMAP , large-scale structure, and supernova data, we can still put a strong constraint on the dark energy equation of state, w = -1.08 ± 0.12. For a flat universe, the combination of WMAP and other astronomical data yield a constraint on the sum of the neutrino masses, m ν < 0.66 eV (95%CL). Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps using Minkowski functionals, the bispectrum, trispectrum, and a new statistic designed to detect large-scale anisotropies in the fluctuations.

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