Wilkinson Microwave Anisotropy Probe DR4

The data made available through this page has been updated. The most recent version of this data may be accessed through https://lambda.gsfc.nasa.gov/product/wmap/current/"

DR4 Cosmological Parameters

Analysis of the WMAP data involved the computation of cosmological parameters assuming a variety of models and including a variety of datasets in addition to the WMAP dataset. The various model/dataset combinations that were tested are displayed in a matrix; the combinations that were analyzed have links in the corresponding cells to individual display pages that show the cosmological parameters computed using that combination of model and dataset. A printable version of each list of parameters is made available as a Postscript file through a link its corresponding the individual display page.

Mnemonics are used to identify the models and datasets in the table and the individual model/dataset displays. The following table translate the mnemonics:

¹ RECFAST is the code included in the Code for Anisotropies in the Microwave Background (CAMB) that calculates the fractional ionization of the light elements in the universe for a range of redshifts around z=1000 for the purpose of determining the cosmic microwave background power spectra.

As mentioned previously, each model/dataset combination has an individual display page that shows the WMAP measurements of the cosmological parameters, with a link to a Postscript file showing the same parameters. These display pages also contain links to files containing WMAP's best fit C_l's, best fit matter power spectra, and Monte Carlo Markov Chains. The Markov Chain are supplied in a compressed tarball that contains a README file describing the contents. The spectra files contain:

• Best fit C_l scalar files contain four columns: l, TT, EE, and TE. The tensor and total files contain five columns: l, TT, EE, BB, and TE. The C_l columns are scaled: T₀² l (l + 1) C_l / 2&pi in µK²;
• Best fit matter power spectra files contain two columns. The first column is k/h in units of Mpc^-1. The second column is the linear matter power spectrum P(k), defined such that the variance is: σ² = (2π)^-3 ∫d³k P(k)

Some of the Markov Chains are flagged as "post-processed". These chains have been constructed from chains originally run with a different data combination. Importance sampling (Lewis & Bridle, 2002) was used to reweight the original chain for the new dataset. The new distribution is checked against the original chain to determine if the statistics can be trusted. Some of the contents of these chains differ from normal chains:

• Weights:
  • The usual 'weight' file appears. It has non-integer entries, as the original weights have been scaled to correspond to the new data set.
  • An additional file 'weight_old' appears. This corresponds to the weight file of the original data set, and is not required for analysis of this chain.
• Likelihoods:
  • The 'lnlike' file contains the -log likelihood of the ORIGINAL chain.
  • The 'del_lnlike' file contains the change in -log likelihood from the reweighting step.

To find the -log likelihood of this chain, you should therefore use total lnlike = 'lnlike' + 'delta_lnlike'

Additional Information

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results, N. Jarosik, et.al. (2010)
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Foreground Emission, B. Gold, et.al (2010).
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters, D. Larson, et.al. (2010)
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Assessment of Anomalous CMB Results from WMAP, C. Bennett, et.al. (2010)
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, E. Komatsu, et.al. (2010)
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Mars, Jupiter and Saturn, J. Weiland, et.al (2010).
• The Five-Year WMAP Papers
• The Three-Year WMAP Papers
• The First-Year WMAP Papers
• WMAP Seven Year Explanatory Supplement

• Hicken, et.al., 2009, ApJ, 700, 1097, arXiv:0901.4804
• Kessler, et.al., 2009, ApJS, 185, 32, arXiv:0908.4274
• Lewis, A, and Bridle, S., 2002, PhRvD, 66, 103511, astro-ph/0205436
• Percival, et.al., 2010, MNRAS, 401, 2148, arXiv:0907.1660
• Riess, et.al., 2009, ApJ, 699, 539, arXiv:0905.0695
• Reid, et.al., 2010, MNRAS, 404, 60, arXiv:0907.1659
• Suyu, et.al., 2010, ApJ, 711, 201, arXiv:0910.2773

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