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FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: LIKELIHOODS AND PARAMETERS FROM THE WMAP DATA
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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, Ω Λ = 0.742 ± 0.030, n s = 0.963 +0.014 −0.015 , τ = 0.087 ± 0.017, and σ 8 = 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 / d ln 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.
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“Modern observations have confirmed that the matter content in the present universe is dominantly composed of about 70% dark energy (with P = -ρc 2 ), about 30% of cold dark matter and baryonic matter (with P ≪ ρc 2 ), and a very small fraction of radiation (about 10 -5 in mass density with P = ρc 2 / 3) [49, 50].”
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“For example, as mentioned in Sec. IV, if there exists a cosmological constant as current observations indicated [49, 50], the κR b a A a term in equation (33) gives rise to a photon mass m A = ( κ Λ) 1 / 2 , corresponding to λ A ∼ 10 28 cm (the size of the cosmic horizon).”
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“Given the very small value of a possible cosmological constant in the present universe [49, 50], the effect of a so small photon mass may never be observable, unless the universe has a nonzero net charge (Sec. VI).”
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“The requirement that ω A ( z = 0) = Ω A < Ω m provides the first constraint on the value of y”
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Self-citation
Metadata
- Authors
- Dunkley, J., Komatsu, E., Nolta, M. R., Spergel, D. N., Larson, D., Hinshaw, G., Page, L., Bennett, C. L., Gold, B., Jarosik, N., Weiland, J. L., Halpern, M., Hill, R. S., Kogut, A., Limon, M., Meyer, S. S., Tucker, G. S., Wollack, E., & Wright, E. L.
- Affiliations
- Princeton University (US)
- The University of Texas at Austin (US)
- University of Toronto (CA)
- Johns Hopkins University (US)
- Goddard Space Flight Center (US)
- Adnet Systems (United States) (US)
- University of British Columbia (CA)
- Columbia University (US)
- University of Chicago (US)
- Brown University (US)
- University of California, Los Angeles (US)
- Corresponding author
- Dunkley, J.
- Weiland, J. L.
- ORCID
- Venue
- The Astrophysical Journal Supplement Series
- Publisher
- American Astronomical Society
- Published
- 2009-02-01
- Volume
- 180
- Issue
- 2
- Pages
- 306-329
- ISSN
- 0067-0049 (ISSN-L)
- 1538-4365
- OpenAlex
- W2136696603
- Cited by
- 1,787
- References
- 335
- Citations by year
- 2026: 7 · 2025: 19 · 2024: 25 · 2023: 35 · 2022: 28 · 2021: 29 · 2020: 27 · 2019: 27 · 2018: 34 · 2017: 27 · 2016: 65 · 2015: 50 · 2014: 60 · 2013: 105 · 2012: 142
- FWCI
- 189.43
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Astrophysical Journal Supplement Series (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Keywords
- cosmic microwave background, cosmological parameter constraints, cosmic microwave background anisotropies, CMB polarization, reionization optical depth, reionization redshift, effective number of relativistic species, cosmic neutrino background, tensor-to-scalar ratio, dark energy equation of state
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