Asymptotic behavior of the Einstein-Yang-Mills-dilaton system for a closed Friedmann-Lemaitre universe Original Research Article

We study the coupled Einstein-Yang-Mills-dilaton (EYMD) equations for a Friedmann-Lemaitre universe with constant curvature k = 1. As a first step the 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. This is achieved with the help of an investigation of the critical points of the dynamical system on a compactified extension of the phase space.