Realistic compactification in spatially flat vacuum cosmological models in cubic Lovelock gravity: High-dimensional case

Abstract

We investigate possible regimes in spatially flat vacuum cosmological models in cubic Lovelock gravity. The spatial section is a product of three- and extra-dimensional isotropic subspaces. This is the second paper of the series and we consider D=5 and general D>=6 cases here. For each D case we found critical values for $α$ (Gauss-Bonnet coupling) and $β$ (cubic Lovelock coupling) which separate different dynamical cases and study the dynamics in each region to find all regimes for all initial conditions and for arbitrary values of $α$ and $β$. The results suggest that for D>=3 there are regimes with realistic compactification originating from `generalized Taub' solution. The endpoint of the compactification regimes is either anisotropic exponential solution (for $α> 0$, $μ\equiv β/α^2 < μ_1$ (including entire $β< 0$)) or standard Kasner regime (for $α> 0$, $μ> μ_1$). For D>=8 there is additional regime which originates from high-energy (cubic Lovelock) Kasner regime and ends as anisotropic exponential solution. It exists in two domains: $α> 0$, $β< 0$, $μ\leqslant μ_4$ and entire $α> 0$, $β> 0$. Let us note that for D>=8 and $α> 0$, $β< 0$, $μ< μ_4$ there are two realistic compactification regimes which exist at the same time and have two different anisotropic exponential solutions as a future asymptotes. For D>=8 and $α> 0$, $β> 0$, $μ< μ_2$ there are two realistic compactification regimes but they lead to the same anisotropic exponential solution. This behavior is quite different from the Einstein-Gauss-Bonnet case. There are two more unexpected observations among the results -- all realistic compactification regimes exist only for $α> 0$ and there is no smooth transition from high-energy Kasner regime to low-energy one with realistic compactification.