Wilkinson Microwave Anisotropy Probe

Product Name
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.

This table is formatted somewhat differently that it has been in the past. In most cases, parameters including the H0 and BAO datasets were computed for each model/dataset combination shown in the table by extending the processing for the displayed combinations. Therefore, these parameters are displayed on each subpage instead of these two datasets populating this table. Where available, a single set of chains for the four permutations are provided (combination, combo+HO, combo+BAO, and combo+BAO+H0).

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

Mnemonic Description Mnemonic Description
LCDM ΛCDM ISO+CORR Anticorrelated CDM isocurvature.
OLCDM ΩK allowed to vary. ISO+UNCORR Uncorrelated CDM isocurvature.
WACDM Time-dependent dark energy equation of state, given by
w(a) = w0 + wa (1 - a)
MNU Massive neutrinos.
WCDM Dark energy equation of state (w) allowed
to vary.
RUN Running spectral index.
OWCDM ΩK and w allowed to vary. NREL Number of relativistic species.
YHE ΛCDM with a variable primordial Helium fraction TENS Tensor modes.
Mnemonic Description
WMAP9 WMAP nine year data set
ACT Atacama Cosmology Telescope
BAO Baryonic Acoustic Oscillations (Percival, et al., 2009)
H0 Hubble constant (Riess, et al., 2009)
SNLS3 Supernova Legacy Survey three year sample
SPT South Pole Telescope

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 or redshifts around z=1000 for the purpose of determining the cosmic microwave background power spectra.

As mentioned previously, each displayed 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 Cl'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 Cl 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 Cl columns are scaled: T02 l (l + 1) Cl / 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)

Note regarding baryon drag epoch redshift and BAO constraints:

The baryon drag epoch redshift (zd), sound horizon (rs), and quantities measured in BAO surveys (e.g., rs/Dv) that are reported in the WMAP 9-year parameter tables were calculated using the approximation from Eisenstein & Hu (1998). This was done to be consistent with results reported by BAO surveys at the time. More recent results have typically been reported using a more accurate calculation of zd, for instance using CAMB. This results in an increase in rs by around 2.5% for the ΛCDM model. This correction is discussed in more detail in Appendix B of Hamann et al. (2010).

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A service of the HEASARC and of the Astrophysics Science Division at NASA/GSFC
Goddard Space Flight Center, National Aeronautics and Space Administration
HEASARC Director: Dr. Alan P. Smale
LAMBDA Director: Dr. Eric R. Switzer
NASA Official: Dr. Eric R. Switzer
Web Curator: Mr. Michael R. Greason