Moncrief The main aim of this project is to develop a rigorous approach to inhomogeneous cosmology on a wide variety of possible spacetime manifolds and with a variety of physically interesting matter sources and to investigate potential applications of this theory. As a first step Vincent Moncrief plans to complete his investigations of the long-time existence of large families of inhomogeneous, non-symmetric, vacuum spacetimes which explode from a big bang singularity in the past and expand to infinite volume in the future. These spacetimes, though representing certain sufficiently small (though fully non-linear) perturbations of known reference solutions, can have arbitrarily large spacetime curvatures in the early stages of expansion. The next step will be to include a variety of interesting matter sources in the analysis and attempt to extend the long-time-existence results to non-vacuum solutions containing, e.g., electromagnetic and Yang-Mills fields, perfect and Vlasov fluids and perhaps imperfect fluids of stable-causal type.
This research will clarify the foundations of modern gravitation theory and cosmology. ***
