On `Graceful Exit' from inflationary phase in two-dimensional Liouville String Cosmology

TL;DR

This paper explores two-dimensional Liouville string cosmology, demonstrating a universe that undergoes inflation and a graceful exit, with a bounded string coupling and matter influencing the dynamics, aligning with phenomenological expectations.

Contribution

It introduces a numerical analysis showing how time identification with the Liouville mode leads to a realistic cosmological evolution with inflation and exit in a super-critical string framework.

Findings

Universe exhibits inflation and graceful exit behavior.

String coupling remains bounded during exit.

Vacuum energy depends on initial conditions.

Abstract

Within the context of a super-critical (Liouville) string, we discuss (target-space) two-dimensional string cosmology. A numerical analysis indicates that the identification of time with the Liouville mode results in an expanding universe with matter which exhibits an inflationary phase, and `graceful exit' from it, tending asymptotically to a flat-metric fixed point.This fixed point is characterized by a dilaton configuration which, depending on the initial conditions, either decreases linearly with the cosmic time, or is a finite constant. This implies that, in contrast to the critical string case, the string coupling remains bounded during the exit from the inflationary phase, and, thus, the pertinent dynamics can be reliably described in terms of a tree-level string effective action. The r\^ole of matter in inducing such phenomena is emphasized. It is also interesting to note that the asymptotic value of the vacuum energy, which in the $\sigma$-model framework is identified with the `running' central charge deficit, depends crucially on the set of initial conditions. Thus, although preliminary, this toy model seems to share all the features expected to characterize a phenomenologically acceptable cosmological string model.