Abstract
Title: "Stability issues of multidimensional gravitational models with R^4 scalar curvature nonlinearities"
Abstract:
Subject of the talk is a multidimensional gravitational model with
scalar curvature nonlinearity R^4. It is assumed that the higher
dimensional spacetime manifold of this model undergoes a spontaneous
compactification to a manifold with warped product structure. The main
attention is paid to the stability of the extra-dimensional factor
spaces and it is shown that for certain parameter regions the system
allows for a freezing stabilization of these spaces. The most
interesting fact which is demonstrated is a dependence of the stability
region (in parameter space) on the total dimension D=dim(M) of the
higher dimensional spacetime M. For D>8 the stability region consists of
a single (absolutely stable) sector which is shielded from a conformal
singularity (and an antigravity sector beyond it) by a potential barrier
of infinite height and width. This sector is smoothly connected with the
stability region of a curvature-linear model. For D<8 an additional
(metastable) sector exists which is separated from the conformal
singularity by a potential barrier of finite height and width so that
systems in this sector are prone to collapse into the conformal
singularity. This second sector is not smoothly connected with the first
(absolutely stable) one. Several limiting cases and the possibility for
inflation are discussed. (hep-th/0409112)