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 $\alpha$ (Gauss-Bonnet coupling) and $\beta$ (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 $\alpha$ and $\beta$. 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 $\alpha >0$, $\mu \equiv \beta /{\alpha }^2<{\mu }_1$ (including entire $\beta <0$)) or standard Kasner regime (for $\alpha >0$, $\mu >{\mu }_1$). 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: $\alpha >0$, $\beta <0$, $\mu ⩽{\mu }_4$ and entire $\alpha >0$, $\beta >0$. Let us note that for D>=8 and $\alpha >0$, $\beta <0$, $\mu <{\mu }_4$ 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 $\alpha >0$, $\beta >0$, $\mu <{\mu }_2$ 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 $\alpha >0$ and there is no smooth transition from high-energy Kasner regime to low-energy one with realistic compactification.

34 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1804.06934

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• On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity