Asymptotic Behavior of the Einstein-Yang-Mills-Dilaton System for a Closed Friedmann-Lemaitre Universe

TL;DR

This paper investigates the long-term behavior of solutions to the Einstein-Yang-Mills-Dilaton equations in a closed universe, revealing the absence of inflationary phases under specific conditions through analytical and numerical analysis.

Contribution

It provides a detailed analysis of the EYMD system in a closed universe with constant curvature, focusing on the case with zero dilaton potential and cosmological constant, including phase portraits and solution behaviors.

Findings

No inflationary stages occur in this model.

Behavior of the scale factor varies with the dilaton coupling constant.

Phase portraits illustrate the evolution of the dilaton field.

Abstract

We study the coupled Einstein-Yang-Mills-Dilaton (EYMD) equations for a Fried\-mann-Le\-mai\-tre universe with constant curvature $k=1$. Our detailed analysis is restricted to the case where the dilaton potential and the cosmological constant vanish. Also assuming a static gauge field, we present analytical and numerical results on the behavior of solutions of the EYMD equations. For different values of the dilaton coupling constant we analyze the phase portrait for the time evolution of the dilaton field and give the behavior of the scale factor. It turns out that there are no inflationary stages in this model.