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

Sergey A. Pavluchenko

doi:10.1140/epjc/s10052-018-6099-z

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2018) 78: 611
https://doi.org/10.1140/epjc/s10052-018-6099-z

Regular Article - Theoretical Physics

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

Sergey A. Pavluchenko^*

Programa de Pós-Graduação em Física, Universidade Federal do Maranhão (UFMA), São Luís, Maranhão, 65085-580, Brazil

^* e-mail: sergey.pavluchenko@gmail.com

Received: 5 July 2018
Accepted: 22 July 2018
Published online: 31 July 2018

Abstract

In this paper we perform systematic investigation of all possible regimes in spatially flat vacuum cosmological models in cubic Lovelock gravity. The spatial section is considered as a product of three- and extra-dimensional isotropic subspaces, and the former represents our Universe. As the equations of motion are different for $$D=3, 4, 5$$ and general $D \ge 6$ cases, we considered them all separately. This is the second paper of the series, and we consider $$D=5$$ and general $D \ge 6$ 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, isotropic and anisotropic exponential solutions, 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 in all $D \ge 3$ there are regimes with realistic compactification originating from so-called “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 $D \ge 8$ there is additional regime which originates from high-energy (cubic Lovelock) Kasner regime and ends as anisotropic exponential solution. It exists in two domains: $\alpha > 0$ , $\beta < 0$ , $\mu \le \mu _4$ and entire $\alpha > 0$ , $\beta > 0$ . Let us note that for $D \ge 8$ 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 $D \ge 8$ 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 the low-energy regime with realistic compactification.