Illuminating the background : topics in cosmic microwave background polarization research

The cosmic microwave background provides a wealth of information about the origin and history of the universe. The statistics of the anisotropy and the polarization of the cosmic microwave background, among other things, can tell us about the distribution of matter, the redshift of reionization, and the nature of the primordial fluctuations. From the lensing of cosmic microwave background due to intervening matter, we can extract information about neutrinos and the equation of state of dark energy. A measurement of the large angular scale B- mode polarization has been called the "smoking gun'' of inflation, a theory that describes a possible early rapid expansion of the universe. The focus of current experiments is to measure this B-mode polarization, while several experiments, such as POLARBEAR, are also looking to measure the lensing of the cosmic microwave background. This dissertation will discuss several different topics in cosmic microwave background polarization research. I will make predictions for future experiments and I will also show analysis for two current experiments, POLARBEAR and BICEP. I will show how beam systematics affect the measurement of cosmological parameters and how well we must limit these systematics in order to get unbiased constraints on cosmological parameters for future experiments. I will discuss a novel way of using the temperature-polarization cross-correlation to constrain the amount of inflationary gravitational waves. Through Markov Chain Monte Carlo methods, I will determine how well future experiments will be able to constrain the neutrino masses and their degeneracy parameters. I will show results from current data analysis and calibration being done on the Cedar Flat deployment for the POLARBEAR experiment which is currently being constructed in the Atacama desert in Chile. Finally, I will analyze the claim of detection of cosmological birefringence in the BICEP data and show that there is reason to believe it is due to systematic effects in the dat