Cosmological solutions, p-branes, and the Wheeler-DeWitt equation
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The low energy effective actions which arise from string theory or (Formula presented)-theory 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 (Formula presented) Toda equations. The solutions of the Wheeler-DeWitt equation in minisuperspace are obtained for some of the simpler cosmological models by introducing intertwining operators that generate canonical transformations which map the theories into free theories. We study the cosmological properties of these solutions, and also briefly discuss generalized Brans-Dicke models in our framework. The cosmological models are closely related to (Formula presented)-brane solitons, which we discuss in the context of the (Formula presented) Toda equations. We give the explicit solutions for extremal multi-charge (Formula presented)-branes in the truncated system described by the (Formula presented) Toda equations. 1998 The American Physical Society.