Stringy Toda Cosmologies

TL;DR

This paper explores string-inspired cosmological models with integrable equations of motion, revealing singular solutions and novel behaviors like shrinking spatial sections despite winding modes, and discusses extensions via dualities.

Contribution

It introduces a specific stringy cosmology based on the $SU(3)$ Toda molecule, providing explicit solutions and analyzing their properties, including singularities and unexpected spatial behaviors.

Findings

All solutions are singular.

Some spatial sections shrink to a point despite winding modes.

Extensions via STU dualities can generate more general solutions.

Abstract

We discuss a particular stringy modular cosmology with two axion fields in seven space-time dimensions, decomposable as a time and two flat three-spaces. The effective equations of motion for the problem are those of the $SU(3)$ Toda molecule, and hence are integrable. We write down the solutions, and show that all of them are singular. They can be thought of as a generalization of the Pre-Big-Bang cosmology with excited internal degrees of freedom, and still suffering from the graceful exit problem. Some of the solutions however show a rather unexpected property: some of their spatial sections shrink to a point in spite of winding modes wrapped around them. We also comment how more general, anisotropic, solutions, with fewer Killing symmetries can be obtained with the help of STU dualities.