MG11 
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Abstract

Stability issues of multidimensional models with R^n scalar curvature non linearities

Subject of the talk is a multidimensional gravitational toy model with scalar curvature nonlinearity R^4. In a simplified phenomenological appraoch it is assumed that the higher dimensional spacetime manifold of this model undergoes a spontaneous compactification to a manifold with warped product structure. The interplay of scalar curvature nonlinearity and warped product structure leads to certain parameter space regions which allow for a freezing stabilization of the extra-dimensional factor spaces. In contrast to earlier considered models with R^2 nonlinearities, the R^4 models possess not only absolutely stable sectors, but also metastable sectors with configurations which are prone to collapse into conformal singularities. 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 a sector with wrong sign gravitational coupling 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.