Simulating Structure Formation with Ultra-light Bosonic Dark Matter

Despite being a cornerstone of the standard model of cosmology, the exact nature of dark matter (DM) remains unknown. The lack of evidence for weakly interacting massive particles that could constitute DM is generating increasing interest in alternative candidates. These include the theoretically well-motivated QCD axion, which solves the strong CP problem, and axion-like particles generically arising in string theories. This thesis focuses on the latter. If non-gravitational interactions can be neglected, this form of DM is known as fuzzy dark matter (FDM). While indistinguishable from cold DM on large scales, these ultra-light (pseudo-)scalar particles are thought to form a coherent state on galactic scales. Wave effects then induce a Jeans scale below which gravitational collapse is suppressed. As the corresponding model dependent phenomena on (sub-)galactic scales are due to highly non-linear dynamics, numerical simulations are of paramount importance in order to make stringent model-dependent predictions that can discriminate between different DM theories. This thesis contributes to the endeavor of linking theoretical FDM models to astrophysical observations by defining and quantifying phenomenological predictions. In doing so, the author utilized different numerical schemes in order to discretize the Schroedinger-Poisson system which governs the non-relativistic, Newtonian dynamics of FDM. The overall aim of these simulations is to constrain the FDM mass as the single parameter of the theory