The quantum mechanics of spatially homogenous cosmological models is important both as a paradigm for quantum gravity and as an arena for the study of quantum effects in the Early Universe. The wave function of the Universe may be obtained either as the solution to the Wheeler-DeWitt equation or from a path integral formulation. For more than two or three degrees of freedom, neither analytic nor numerical differencing methods can be used. Dr. Berger will apply several numerical simulation methods which yield wave functions in many contexts (e.g. for multi-electron atoms, condensed matter, and dissolved electron in fluid systems with an arbitrary number of degrees of freedom) to quantized cosmological models. The physical behavior of the simulations will be examined particularly with regard to the presence of inflation, fluctuations, and singularity avoidance. Formal issues will be pursued with a lattice simulation of quantum gravity as the eventual goal.
