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FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE * OBSERVATIONS: LIKELIHOODS AND PARAMETERS FROM THE WMAP DATA

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J. Dunkley1,2,3, E. Komatsu4, M. R. Nolta5, D. N. Spergel2,6, D. Larson7, G. Hinshaw8, L. Page1, C. L. Bennett7, B. Gold7, N. Jarosik1, J. L. Weiland9, M. Halpern10, R. S. Hill9, A. Kogut8, M. Limon11, S. S. Meyer12, G. S. Tucker13, E. Wollack8 and E. L. Wright14

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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, ΩΛ = 0.742 ± 0.030, ns = 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 dns /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.


Footnote
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.
Keywords

cosmic microwave background; cosmology: observations; early universe; polarization


Dates

Issue 2 (2009 February)

Received 2008 March 4, accepted for publication 2008 July 23

Published 2009 February 11



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