De Sitter stability in quadratic gravity

Quadratic curvature corrections to Einstein-Hilbert action lead in general to higher-order equations of motion, which can induced instability of some unperturbed solutions of General Relativity. We study conditions for stability of de Sitter cosmological solution. We argue that simple form of this condition known for FRW background in 3+1 dimensions changes seriously if at least one of these two assumptions is violated. In the present paper the stability conditions for de Sitter solution have been found for multidimensional FRW background and for Bianchi I metrics in 3+1 dimensions.Comment: 12 pages with 4 figures; references adde

Effects of spatial curvature and anisotropy on the asymptotic regimes in Einstein-Gauss-Bonnet gravity

In this paper we address two important issues which could affect reaching the exponential and Kasner asymptotes in Einstein-Gauss-Bonnet cosmologies -- spatial curvature and anisotropy in both three- and extra-dimensional subspaces. In the first part of the paper we consider cosmological evolution of spaces being the product of two isotropic and spatially curved subspaces. It is demonstrated that the dynamics in $D=2$ (the number of extra dimensions) and $D \geqslant 3$ is different. It was already known that for the $\Lambda$-term case there is a regime with "stabilization" of extra dimensions, where the expansion rate of the three-dimensional subspace as well as the scale factor (the "size") associated with extra dimensions reach constant value. This regime is achieved if the curvature of the extra dimensions is negative. We demonstrate that it take place only if the number of extra dimensions is $D \geqslant 3$. In the second part of the paper we study the influence of initial anisotropy. Our study reveals that the transition from Gauss-Bonnet Kasner regime to anisotropic exponential expansion (with expanding three and contracting extra dimensions) is stable with respect to breaking the symmetry within both three- and extra-dimensional subspaces. However, the details of the dynamics in $D=2$ and $D \geqslant 3$ are different. Combining the two described affects allows us to construct a scenario in $D \geqslant 3$, where isotropisation of outer and inner subspaces is reached dynamically from rather general anisotropic initial conditions.Comment: 22 pages, 3 figure