Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions. Vacuum case

Abstract

In this paper we perform a systematic study of vacuum spatially flat ((3+D)+1)-dimensional Einstein-Gauss-Bonnet cosmological models. We consider models which topologically are the product of two flat isotropic subspaces with different scale factors. One of these subspaces is 3D and represents our space and the other is D-dimensional and represents extra dimensions. We consider no ansatz of the scale factors, which makes our results quite general. With both Einstein-Hilbert and Gauss-Bonnet contributions in play, the cases with D=1, D=2, D=3 and $D⩾4$ have different dynamics due to different structure of the equations of motion. We analytically study equations of motion in all cases and describe all possible regimes. It appears that the only regimes with nonsingular future asymptotes are the Kasner regime in GR as well as exponential regimes. As of the past asymptotes, for a smooth transition only Kasner regime in Gauss-Bonnet is an option. With that at hand, we are down only to two viable regimes -- "pure" Kasner regime (transition from high- to low-energy Kasner regime) and a transition from high-energy Kasner to anisotropic exponential solution. It appears that these regimes take place for different signs of the Gauss-Bonnet coupling $\alpha$: "pure" Kasner regime occur for $\alpha >0$ at low D and $\alpha <0$ for high D; anisotropic exponential regime is reached only for $\alpha >0$. So if we restrain ourselves with $\alpha >0$ solutions, the only late-time regimes are Kasner for D=1, 2 and anisotropic exponential for $D⩾2$. Also, low-energy Kasner regimes ($a(t)\propto t^p$) have expansion rates for (3+1)-dimensional subspace ("our Universe") ranging from p=0.5 (D=1) to $p=1/\sqrt{3}\approx 0.577$ ($D\to \infty$), which contradicts with dust-dominated Friedmann prediction (p=2/3).

34 pages, 7 figures, 7 tables

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• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: Low-dimensional $\Lambda$-term case
• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: High-dimensional $\Lambda$-term case
• Effects of spatial curvature and anisotropy on the asymptotic regimes in Einstein-Gauss-Bonnet gravity
• Cosmological solutions in Einstein-Gauss-Bonnet gravity with static curved extra dimensions
• Realistic Compactification Models in Einstein-Gauss-Bonnet Gravity
• Violation of Hod's Conjecture and Probing it with Optical properties of a 5-D black hole in Einstein Gauss-Bonnet Bumblebee theory of gravity
• Dynamics of the cosmological models with perfect fluid in Einstein-Gauss-Bonnet gravity: low-dimensional case
• Realistic compactification in spatially flat vacuum cosmological models in cubic Lovelock gravity: High-dimensional case
• Realistic compactification in spatially flat vacuum cosmological models in cubic Lovelock gravity: Low-dimensional case
• Cosmological Models in Lovelock Gravity: An Overview of Recent Progress
• On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity