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

TL;DR

This paper explores the dynamics of high-dimensional vacuum cosmological models in cubic Lovelock gravity, identifying regimes that lead to realistic compactification and analyzing their dependence on coupling parameters.

Contribution

It provides a detailed analysis of the regimes in cubic Lovelock gravity for D=5 and D>=6, revealing new compactification behaviors and critical parameter values.

Findings

Existence of regimes with realistic compactification from generalized Taub solutions.

Different asymptotic behaviors depending on coupling parameters and dimensions.

Discovery of multiple regimes in high-dimensional cases with unique future asymptotes.

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: $\alpha > 0$, $\beta < 0$, $\mu \leqslant \mu_4$ 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.