First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Parameter Estimation Methodology

We describe our methodology for comparing the WMAP measurements of the cosmic microwave background (CMB) and other complementary data sets to theoretical models. The unprecedented quality of the WMAP data, and the tight constraints on cosmological parameters that are derived, require a rigorous analysis so that the approximations made in the modeling do not lead to significant biases. We describe our use of the likelihood function to characterize the statistical properties of the microwave background sky. We outline the use of the Monte Carlo Markov Chains to explore the likelihood of the data given a model to determine the best fit cosmological parameters and their uncertainties. We add to the WMAP data the l & 700 CBI and ACBAR measurements of the CMB, the galaxy power spectrum at z ∼ 0 obtained from the 2dF galaxy redshift survey (2dFGRS), and the matter power spectrum at z ∼ 3 as measured with the Lyman α forest. These last two data sets complement the CMB measurements by probing the matter power spectrum of the nearby universe. Combining CMB and 2dFGRS requires that we include in our analysis a model for galaxy bias, redshift distortions, and the nonlinear growth of structure. We show how the statistical and systematic uncertainties in the model and the data are propagated through the full analysis. 1 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. Dept of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 Chandra Fellow Code 685, Goddard Space Flight Center, Greenbelt, MD 20771 Dept. of Physics and Astronomy, University of British Columbia, Vancouver, BC Canada V6T 1Z1 Dept. of Physics, Jadwin Hall, Princeton, NJ 08544 Depts. of Astrophysics and Physics, EFI and CfCP, University of Chicago, Chicago, IL 60637 National Research Council (NRC) Fellow Dept. of Physics, Brown University, Providence, RI 02912 UCLA Astronomy, PO Box 951562, Los Angeles, CA 90095-1562