The current cosmological concordance model states that the fluctuations in the Cosmic Microwave Background (CMB) should be Gaussian and isotropic. However, many studies claim to have found small deviations from this theory. One such deviation is the apparent existence of hemispherical power asymmetry: One hemisphere of the CMB appears to contain stronger fluctuations than the other. As of yet, it is not clear whether this is a statistical fluke, a systematic effect, or a genuine violation of the cosmological principle. Current studies are either limited to studying structures on large scales due to the poor computational scaling of O(Npix^3) (Hoftuft et al., 2009, Eriksen et al., 2007, Gordon, 2007), make use of approximate methods (Hanson & Lewis, 2009, Bennett et al., 2010), or focus on non-parametric statistics (Hansen et al., 2009).
A computationally efficient method for fully exact, Bayesian analysis of the hemispherical CMB power asymmetry has been developed in this thesis, based on the CMB Gibbs sampling algorithm (Wandelt et al., 2004, Jewell et al., 2004). With a computational scaling of O(Npix^(3/2)), the method is able to explore current and future CMB observations at full resolution. Probing for the presence of asymmetry at l >= 1000 is fully realistic for the upcoming Planck data. In this thesis, a dipole modulation field model gets particular attention. However, the computational foundation is also laid for exploring moregeneral models than what has previously been possible. Models with arbitrary azimuthally symmetric modulation fields or scale-dependent modulation strength can be fitted to data at the same computational cost.
The complete algorithm has been implemented from scratch in Python and thoroughly tested on simulations. A direct comparison is made with the results of Hoftuft et al. on low resolution data. Some preliminary results of analysis of full resolution WMAP 7-year data are also presented. The preliminary findings are consistent with the earlier studies, indicating the presence of asymmetry on scales up to l = 600. In particular, the preferred direction is consistent with earlier results.
The code is believed to be ready for a more thorough study of WMAP data, although a few final checks are outlined that should be carried out first. As a direct consequence of reviewing the CMB Gibbs sampling algorithm in detail, a couple of minor flaws were found in the existing CMB Gibbs sampler Commander.