Effects of spatial curvature and anisotropy on the asymptotic regimes in Einstein-Gauss-Bonnet gravity

Abstract

In this paper we address two important issues which could affect reaching the exponential and Kasner asymptotes in Einstein-Gauss-Bonnet cosmologies -- spatial curvature and anisotropy in both three- and extra-dimensional subspaces. In the first part of the paper we consider cosmological evolution of spaces being the product of two isotropic and spatially curved subspaces. It is demonstrated that the dynamics in $D=2$ (the number of extra dimensions) and $D⩾3$ is different. It was already known that for the $\Lambda$-term case there is a regime with "stabilization" of extra dimensions, where the expansion rate of the three-dimensional subspace as well as the scale factor (the "size") associated with extra dimensions reach constant value. This regime is achieved if the curvature of the extra dimensions is negative. We demonstrate that it take place only if the number of extra dimensions is $D⩾3$. In the second part of the paper we study the influence of initial anisotropy. Our study reveals that the transition from Gauss-Bonnet Kasner regime to anisotropic exponential expansion (with expanding three and contracting extra dimensions) is stable with respect to breaking the symmetry within both three- and extra-dimensional subspaces. However, the details of the dynamics in $D=2$ and $D⩾3$ are different. Combining the two described affects allows us to construct a scenario in $D⩾3$, where isotropisation of outer and inner subspaces is reached dynamically from rather general anisotropic initial conditions.

22 pages, 3 figures

References in corpus (15)

• Viscosity Bound and Causality Violation
• A Note on Thermodynamics of Black Holes in Lovelock Gravity
• Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
• Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity
• Black Holes in Pure Lovelock Gravities
• Stationary vs. singular points in an accelerating FRW cosmology derived from six-dimensional Einstein-Gauss-Bonnet gravity
• Cosmic acceleration with a negative cosmological constant in higher dimensions
• A note on differences between (4+1)- and (5+1)-dimensional anisotropic cosmology in the presence of the Gauss-Bonnet term
• On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model
• Asymptotically Flat Radiating Solutions in Third Order Lovelock Gravity
• Cosmological dynamics in higher-dimensional Einstein-Gauss-Bonnet gravity
• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: Low-dimensional $\Lambda$-term case
• Constant volume exponential solutions in Einstein-Gauss-Bonnet flat anisotropic cosmology with a perfect fluid
• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: High-dimensional $\Lambda$-term case
• The dynamics of the flat anisotropic models in the Lovelock gravity. I: The even-dimensional case

Cited by in corpus (16)

• Cosmological solutions in Einstein-Gauss-Bonnet gravity with static curved extra dimensions
• Realistic Compactification Models in Einstein-Gauss-Bonnet Gravity
• Classical evolution of subspaces
• Inhomogeneous compact extra dimensions and de Sitter cosmology
• Dynamic compactification with stabilized extra dimensions in cubic Lovelock gravity
• Some aspects of the cosmological dynamics in Einstein-Gauss-Bonnet gravity
• Dynamics of the cosmological models with perfect fluid in Einstein-Gauss-Bonnet gravity: low-dimensional case
• Anisotropic cosmological dynamics in Einstein-Gauss-Bonnet gravity: an example of dynamical compactification in 7+1 dimensions
• Realistic compactification in spatially flat vacuum cosmological models in cubic Lovelock gravity: High-dimensional case
• Quantum fields in Bianchi type I spacetimes. The Kasner metrc
• Realistic compactification in spatially flat vacuum cosmological models in cubic Lovelock gravity: Low-dimensional case
• Spontaneous symmetry breaking as a result of extra dimensions compactification
• Evolution of sub-spaces at high and low energies
• Cosmological Models in Lovelock Gravity: An Overview of Recent Progress
• Gauss-Bonnet dynamical compactification scenarios and their ghosts in the tensor sectors
• On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity