Cosmological Solutions in String Theories

TL;DR

This paper derives a broad class of exact cosmological solutions in string theory's low-energy limits, describing expanding universes with various spatial geometries and analyzing their behavior when lifted to higher dimensions.

Contribution

It introduces a method to obtain exact cosmological solutions in string theories using Liouville and Toda equations, extending understanding of possible universe evolutions in these models.

Findings

Solutions include flat, spherical, and hyperbolic spatial sections.

Some solutions describe four-dimensional expanding universes.

Analysis of higher-dimensional behavior upon oxidation.

Abstract

We obtain a large class of cosmological solutions in the toroidally-compactified low energy limits of string theories in $D$ dimensions. We consider solutions where a $p$-dimensional subset of the spatial coordinates, parameterising a flat space, a sphere, or an hyperboloid, describes the spatial sections of the physically-observed universe. The equations of motion reduce to Liouville or $SL(N+1,R)$ Toda equations, which are exactly solvable. We study some of the cases in detail, and find that under suitable conditions they can describe four-dimensional expanding universes. We discuss also how the solutions in $D$ dimensions behave upon oxidation back to the $D=10$ string theory or $D=11$ M-theory.