The Stability of Relativistic Fluids in Expanding Spacetimes

Spatially homogeneous and fluid-filled solutions to the Einstein field equations play a distinguished role in the study of relativistic cosmology. In this thesis we investigate the asymptotic behaviour of non-linear, inhomogeneous perturbations of these models using a combination of rigorous analysis and numerical methods. Our main result is a proof of the future non-linear stability of tilted, two fluid Bianchi I models in the presence of a positive cosmological constant. Additionally, we use numerical methods to investigate a type of fluid instability in perturbed FLRW spacetimes. Our numerical results support a longstanding conjecture of Rendall.