Cosmological solutions,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>-branes, and the Wheeler-DeWitt equation

Abstract

The low energy effective actions which arise from string theory or $M$-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 ${E}_{N}$ 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 $p$-brane solitons, which we discuss in the context of the ${E}_{N}$ Toda equations. We give the explicit solutions for extremal multi-charge $(D\ensuremath{-}3)$-branes in the truncated system described by the ${D}_{4}=O(4,4)$ Toda equations.