Qualitative evolution in higher-loop stringcosmology

Abstract

We investigate the evolution of the homogeneous and isotropic universe within the framework of the effective string gravity with string-loop modifications of dilaton couplings. In the case of a barotropic perfect fluid as a non-gravitational source, the set of cosmological equations is presented in the form of a third-order autonomous dynamical system. The cases considered are when this system is integrable in terms of integrals depending on dilaton coupling functions. Without specifying these functions we describe the generic evolution of the universe, using dynamical systems methods. The critical points and their stability are found for all regions of the parameters. The qualitatively different phase-space diagrams are presented for the spatially flat, closed and open universes. The case of the tree-level models is considered separately. The issue of dilaton stabilization is discussed within the framework of the Damour-Polyakov mechanism. No specific forms of string-loop corrections are used and the analysis is applicable to any non-minimally coupled scalar-tensor theory.