Solutions to the Wheeler-Dewitt Equation Inspired by the String Effective Action

TL;DR

This paper derives and solves the Wheeler-DeWitt equation from string theory effective actions, providing exact and approximate solutions for quantum cosmological models like FRW and Bianchi IX universes.

Contribution

It introduces a novel approach to quantum cosmology by deriving the Wheeler-DeWitt equation from string theory and finding exact solutions for complex cosmological models.

Findings

Exact solutions for FRW cosmology derived from string theory

Successive approximation method for more general solutions

Exact solutions for Bianchi IX universe quantum cosmology

Abstract

The Wheeler-DeWitt equation is derived from the bosonic sector of the heterotic string effective action assuming a toroidal compactification. The spatially closed, higher dimensional Friedmann-Robertson-Walker (FRW) cosmology is investigated and a suitable change of variables rewrites the equation in a canonical form. Real- and imaginary-phase exact solutions are found and a method of successive approximations is employed to find more general power series solutions. The quantum cosmology of the Bianchi IX universe is also investigated and a class of exact solutions is found.