In recent years, cosmological science has developed a highly predictive model for the universe on large scales that is in quantitative agreement with a wide range of astronomical observations. While the number and diversity of successes of this model provide great confidence that our general picture of cosmology is correct, numerous puzzles remain. In this dissertation, I analyze the potential of planned and near future galaxy surveys to provide new understanding of several unanswered questions in cosmology, and address some of the leading challenges to this observational program. In particular, I study an emerging technique called cosmic shear, the weak gravitational lensing produced by large scale structure. I focus on developing strategies to optimally use the cosmic shear signal observed in galaxy imaging surveys to uncover the physics of dark energy and the early universe.
In chapter 1 I give an overview of a few unsolved mysteries in cosmology and I motivate weak lensing as a cosmological probe. I discuss the use of weak lensing as a test of general relativity in chapter 2 and assess the threat to such tests presented by our uncertainty in the physics of galaxy formation. Interpreting the cosmic shear signal requires knowledge of the redshift distribution of the lensed galaxies. This redshift distribution will be significantly uncertain since it must be determined photometrically. In chapter 3 I investigate the influence of photometric redshift errors on our ability to constrain dark energy models with weak lensing. The ability to study dark energy with cosmic shear is also limited by the imprecision in our understanding of the physics of gravitational collapse. In chapter 4 I present the stringent calibration requirements on this source of uncertainty. I study the potential of weak lensing to resolve a debate over a long-standing anomaly in CMB measurements in chapter 5. Finally, in chapter 6 I summarize my findings and conclude with a brief discussion of my outlook on the future of weak lensing studies of cosmology
