Dilaton, winding modes and cosmological solutions

TL;DR

This paper reviews cosmological solutions in closed string theory with duality symmetric matter, showing oscillating scale factors influenced by winding modes and dilaton dynamics, with duality symmetry spontaneously broken.

Contribution

It analyzes how winding modes and dilaton fields affect cosmological evolution, revealing oscillatory behaviors and spontaneous duality breaking in string cosmology models.

Findings

Scale factor oscillates between maximum and minimum values.

Winding modes prevent infinite expansion of the universe.

Duality symmetry is spontaneously broken in generic solutions.

Abstract

We review some formal aspects of cosmological solutions in closed string theory with duality symmetric ``matter'' following recent paper with C. Vafa (HUTP-91/A049). We consider two models : when the matter action is the classical action of the fields corresponding to momentum and winding modes and when the matter action is represented by the quantum vacuum energy of the string compactified on a torus. Assuming that the effective vacuum energy is positive one finds that in both cases the scale factor undergoes oscillations from maximal to minimal values with the amplitude of oscillations decreasing to zero or increasing to infinity depending on whether the effective coupling (dilaton field) decreases or increases with time. The contribution of the winding modes to the classical action prevents infinite expansion. Duality is ``spontaneously broken'' on a solution with generic initial conditions.