UC Berkeley

Three decades have passed since the technique of gravitational microlensing was proposed as a means for exoplanet detection, and nearly 200 microlensing exoplanets have been discovered to date.Previously, theoretical studies of the two-body point-mass gravitational lens have primarily focused on the properties of caustics, which are the singularities in the magnification map. The invariances and symmetries of microlensing caustics have led to the identification of physical degeneracies that cause distinctly different lens configurations to give rise to nearly identical observations. Nevertheless, inconsistencies in the application of existing degeneracy theories to observed events indicate that our current theoretical understanding of binary-lens gravitational microlensing, which was largely laid out in the late twentieth century, may in fact be incomplete.

This thesis introduces a novel approach to utilizing Artificial Intelligence as a driver for theoretical explorations, which represents a departure from its traditional role in accelerating empirical discoveries.First, a scalable inference framework is developed for binary-lens microlensing using the technique of Neural Posterior Estimation, which is then applied to model hundreds of simulated microlensing light-curve observations. By examining the large numbers of multi-modal modeling solutions, I propose and subsequently prove the offset degeneracy, which is shown to be ubiquitous in the interpretation of planetary microlensing observations, and unifies two leading types of caustic degeneracies as limiting cases. Motivated by properties of the offset degeneracy, I subsequently propose the generalized perturbative picture for planetary microlensing, which states that the planet can be considered to act as a variable-shear Chang-Refsdal lens on one of the images produced by the host star, leaving the other image largely unaffected. The analytic nature of the Chang-Refsdal lens indicates that the proposed formalism would allow for full magnification maps of the planetary lens to be derived analytically, thereby facilitating the accelerated modeling of observed events. The methodologies and results presented in this thesis may substantially benefit the analysis of the deluge of data expected from the first space-based microlensing survey of the Roman Space Telescope.