Three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Implications for cosmology

D. N. Spergel, R. Bean, O. Doré, M. R. Nolta, C. L. Bennett, J. Dunkley, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. WeilandE. Wollack, E. L. Wright

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A simple cosmological model with only six parameters (matter density, Ωmh2, baryon density, Ωbh 2, Hubble constant, H0, amplitude of fluctuations, σ8, optical depth, τ, and a slope for the scalar perturbation spectrum, ns) 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 bestfit values for cosmological parameters for the power-law flat A cold dark matter (ACDM) model are (Ωmh2, Ωbh2, h, n s, τ, σ8) = (0.1277-0.0079 +0.0080,0.02229 ± 0.00073, 0.732-0.032 +0.031,0.958 ± 0.016, 0.089 ± 0.030, 0.761 -0.048+0.049). 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 (ns = 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, r0.002 < 0.65 (95% CL) and the combination of WMAP and the lensing-normalized SDSS galaxy survey implies r0.002 < 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 ACDM model; however, the improvement in the fit to the WMAP data is only Δχ2 = 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 = -0.967-0.072+0.073. If we assume w = -1, then the deviations from the critical density, ΩK, are small: the combination of WMAP and the SNLS data implies Ωk = -0.011 ± 0.012. The combination of WMAP 3 year data plus the HST Key Project constraint on H0 implies ±k = -0.014 ± 0.017 and ΩA = 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, Σmv < 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 functional, the bispectrum, trispectrum, and a new statistic designed to detect large-scale anisotropies in the fluctuations.

Original languageEnglish (US)
Pages (from-to)377-408
Number of pages32
JournalAstrophysical Journal, Supplement Series
Issue number2
StatePublished - Jun 2007

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmic microwave background
  • Cosmology: observations

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