The dynamics of multidimensional cosmological models in the presence of quantum effects. I. The case FRW ×T D at high temperatures

Abstract

The dynamical system approach is applied to the study of dynamics of multidimensional cosmological models with topology FRW ×TD (D-dimensional torus) in the presence of high-temperature quantum effects. The stability methods developed in the paper of Szydlowski (Gen. Rel. Grav.,20, 221, 1988) are used in the analysis of typical states of the metric in the neighborhood of singularities and for large time values. The problems of dynamical dimensional reduction, structure of singularities, isotropization, etc., are discussed in this context.