Non-singular solutions in multidimensional model with scalar fields and exponential potential

Abstract

Using developed earlier our methods for multidimensional models \cite{M1,M2,M3} a family of cosmological-type solutions in D-dimensional model with two sets of scalar fields \vec{\phi} and \vec{\psi} and exponential potential depending upon \vec{\phi} is considered. The solutions are defined on a product of n Ricci-flat spaces. The fields from \vec{\phi} have positive kinetic terms and \vec{\psi} are "phantom" fields with negative kinetic terms. For vector coupling constant obeying 0< \vec{\lambda}^2 < (D-1)/(D-2) a subclass of non-singular solutions is singled out. The solutions from this subclass are regular for all values of synchronous "time" \tau \in (- \infty, + \infty). For \vec{\lambda}^2 < 1/(D-2) we get an asymptotically accelerated and isotropic expansion for large values of \tau.