COSMOLOGICAL SOLUTIONS, P-BRANES, AND THE WHEELER-DEWITT EQUATION

The low energy effective actions which arise from string theory or M-t heory are considered in the cosmological context, where the graviton, dilaton and antisymmetric tensor field strengths depend only on time. We show that previous results can be extended to include cosmological solutions that are related to the E-N, Toda equations. The solutions o f the Wheeler-DeWitt equation in minisuperspace are obtained for some of the simpler cosmological models by introducing intertwining operato rs that generate canonical transformations which map the theories into free theories. We study the cosmological, properties of these solutio ns, and also briefly discuss generalized Brans-Dicke models in our fra mework. The cosmological models are closely related to p-brane soliton s, which we discuss in the context of the E-N Toda equations. We give the explicit solutions for extremal multi-charge (D-3)-branes in the t runcated system described by the D-4,=0(4,4) Toda equations. [S0556-28 21(98)01806-2].