Integrable Multidimensional Classical and Quantum Cosmology for Intersecting p-branes

TL;DR

This paper develops an integrable multidimensional cosmological model with p-branes, deriving exact classical and quantum solutions using Toda-like representations and orthogonality conditions, advancing understanding of higher-dimensional cosmology.

Contribution

It introduces a new integrable model of multidimensional cosmology with p-branes, providing exact classical and quantum solutions under specific conditions.

Findings

Derived Toda-like Lagrange representation for the model

Obtained exact classical solutions under orthogonality conditions

Presented quantum solutions via the Wheeler-De Witt equation

Abstract

Multidimensional cosmological model describing the evolution of one Einstein space of non-zero curvature and n Ricci-flat internal spaces is considered. The action contains several dilatonic scalar fields and antisymmetric forms. When forms are chosen to be proportional of volume forms of p-brane submanifolds of internal space manifold, the Toda-like Lagrange representation is obtained. Wheeler-De Witt equation for the model is presented. The exact solutions in classical and quantum cases are obtained when dimensions of p-branes and dilatonic couplings obey some orthogonality conditions.