Statistical analysis of the cosmic microwave background: Power spectra and foregrounds.

摘要

In this thesis I examine some of the challenges associated with analyzing Cosmic Microwave Background (CMB) data and present a novel approach to solving the problem of power spectrum estimation, which is called MAGIC (MAGIC Allows Global Inference of Covariance).;In light of the computational difficulty of a brute force approach to power spectrum estimation, I review several approaches which have been applied to the problem and show an example application of such an approximate method to experimental CMB data from the Background Emission Anisotropy Scanning Telescope (BEAST).;I then introduce MAGIC, a new approach to power spectrum estimation; based on a Bayesian statistical analysis of the data utilizing Gibbs Sampling. I demonstrate application of this method to the all-sky Wilkinson Microwave Anistropy Probe WMAP data. The results are in broad agreement with those obtained originally by the WMAP team. Since MAGIC generates a full description of each Cl it is possible to examine several issues raised by the best-fit WMAP power spectrum, for example the perceived lack of power at low ℓ. It is found that the distribution of Cℓ's at low l are significantly non-Gaussian and, based on the exact analysis presented here, the "low quadrupole issue" can be attributed to a statistical fluctuation.;Finally, I examine the effect of Galactic foreground contamination on CMB experiments and describe the principle foregrounds. I show that it is possible to include the foreground components in a self-consistent fashion within the statistical framework of MAGIC and give explicit examples of how this might be achieved. Foreground contamination will become an increasingly important issue in CMB data analysis and the ability of this new algorithm to produce an exact power spectrum in a computationally feasible time, coupled with the foreground component separation and removal is an exciting development in CMB data analysis. When considered with current algorithmic developments such as the ability to include asymmetric beam shapes and deal with polarized data, the future of the Gibbs sampling approach shows great promise.