Weak Gravitational Lensing Diagnostic Tests in Preparation for Stage-IV Cosmic Shear

In the next decade, surveys such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), ESA’s Euclid mission, and NASA’s Nancy Grace Roman Space Telescope, will collect data for billions of galaxies across the sky, mapping the underlying web-like structure of the universe evolving over cosmic time. The exceptional volume and depth of these future datasets are expected to reduce statistical uncertainties dramatically, which brings promise of unprecedented levels of constraining power for major cosmological unknowns: the distribution and composition of dark matter and the nature of dark energy. While cosmological inference will no longer be limited by statistical uncertainty, incomplete and/or incorrect characterization of the systematics induced from astrophysical processes, methodologies, and technological realities may significantly bias or hinder robust scientific analysis. For these upcoming surveys, weak gravitational lensing has been identified as a primary cosmological probe. Weak lensing describes how light traveling along a trajectory from a distant source galaxy interacts with the gravitational potential of intervening matter; this interaction leads to the light traveling along a subtly warped path. For a large sample of galaxies, the statistically coherent shape distortions produced by weak gravitational lensing is unique in that it is not replicated by other known physics, making it a direct probe of the matter distribution of the universe. This phenomenon has been given a name by the cosmological community, now known as cosmic shear. Upcoming surveys have especially stringent requirements for measuring cosmic shear, where the shear signal must be accurate to the 0.1% level. Defining and conducting diagnostic tests is part of the process to meet the aforementioned requirements, where the measured galaxy shapes are assessed in a variety of ways to determine if there are signals that indicate significant errors which could impact cosmological parameter inference. This dissertation focuses on these diagnostic tests, their development, and their applicability for future analyses with data from the LSST.