Cosmological solutions, p-branes and the Wheeler-DeWitt equation

TL;DR

This paper explores cosmological solutions derived from string and M-theory effective actions, connecting them to Toda equations and p-brane solitons, and solves the Wheeler-DeWitt equation for simplified models.

Contribution

It extends previous work to include solutions related to E_N Toda equations and explicitly solves the Wheeler-DeWitt equation for certain cosmological models.

Findings

Solutions related to E_N Toda equations are identified.

Explicit Wheeler-DeWitt solutions for simplified models are obtained.

Connections between cosmological models and p-brane solitons are established.

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 generalised 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-3)-branes in the truncated system described by the D_4 =O(4,4) Toda equations.