Abstract
This thesis is a study of the behaviour of solutions to the Einstein-Maxwell-scalar field equations within the context of cosmology. Using the Fuchsian theorem, we study the singular behaviour of the uncoupled Maxwell equations on Kasner-scalar field backgrounds, and the coupled Einstein-Maxwell-scalar field equations under the assumption of T2 symmetry. Our first result is the proof of a stability theorem for the Maxwell equations on Kasner-scalar field backgrounds. With the heuristics developed from our studies of the uncoupled case in mind, we then go on to prove the main result of this thesis: the asymptotically velocity term dominated behaviour of solutions to the full Einstein-Maxwell-scalar field problem in twisted T2 spacetime. Our result holds where the asymptotic velocity k satisfies 0 < k < min(1, (3p1 - 1)/(1 - p1)). By twisted, we mean a solution to the Einstein equations in T2 symmetry for which the twists are non-constant. We show that in the non-vacuum case, the twists are generically non-constant, and find a condition on the matter field under which the twists can be made constant. We then specialise our results to the Gowdy subcase of T2 symmetry, characterised by the vanishing of the twists, and show that all the results from the T2 case hold in the Gowdy case provided one places certain restrictive assumptions on the electromagnetic field. In the Gowdy case, our results hold under the weaker restriction 0 < k < min(1, (3p1 - 1)/(1 - p1)).