Regular Cosmological Examples of Tree-Level Dilaton-Driven Models

TL;DR

This paper presents analytic, non-singular solutions in tree-level string cosmology with a homogeneous dilaton and inhomogeneous metric, demonstrating regular curvature and dilaton behavior without higher-order corrections.

Contribution

It provides explicit inhomogeneous solutions with regular curvature and dilaton fields in the minimal string effective action, highlighting a non-singular dilaton growth phase.

Findings

Curvature invariants are bounded and regular in time and space.

Dilaton coupling and energy density are homogeneous and regular.

Solutions exhibit a non-singular, growing dilaton phase without higher curvature corrections.

Abstract

We construct some examples of analytic solutions of the low energy (i.e. tree-level) string cosmological effective action. We work with the ``minimal'' field content (i.e. graviton and dilaton) in the absence of any dilaton potential. Provided the metric is sufficiently inhomogeneous we find solutions whose curvature invariants are bounded and everywhere defined in time and space. The dilaton coupling and its associated energy density are regular and homogeneous. A phase of growing (and non-singular) dilaton coupling compatible with the regularity of the curvature invariants without the addition of higher curvature (or higher genus) corrections to the tree-level effective action. We discuss the symmetries of the obtained solutions.