Cosmological Models in Lovelock Gravity: An Overview of Recent Progress

Abstract

In the current review, we provide a summary of the recent progress made in the cosmological aspect of extra-dimensional Lovelock gravity. Our review covers a wide variety of particular model/matter source combinations: Einstein--Gauss--Bonnet as well as cubic Lovelock gravities with vacuum, cosmological constant, perfect fluid, spatial curvature, and some of their combinations. Our analysis suggests that it is possible to set constraints on the parameters of the above-mentioned models from the simple requirement of the existence of a smooth transition from the initial singularity to a realistic low-energy regime. Initially, anisotropic space naturally evolves into a configuration with two isotropic subspaces, and if one of these subspaces is three-dimensional and is expanding while another is contracting, we call it realistic compactification. Of course, the process is not devoid of obstacles, and in our paper, we review the results of the compactification occurrence investigation for the above-mentioned models. In particular, for vacuum and $\Lambda$-term EGB models, compactification is not suppressed (but is not the only possible outcome either) if the number of extra dimensions is $D⩾2$; for vacuum cubic Lovelock gravities it is always present (however, cubic Lovelock gravity is defined only for $D⩾3$ number of extra dimensions); for the EGB model with perfect fluid it is present for $D=2$ (we have not considered this model in higher dimensions yet), and in the presence of spatial curvature, the realistic stabilization of extra dimensions is always present (however, such a model is well-defined only in $D⩾4$ number of extra dimensions).

28 pages, 8 figures, 1 table; published within the Special Issue "Cosmological Models of the Universe'' of the Universe

References in corpus (20)

• 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
• Shock Formation in Lovelock Theories
• 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
• The dynamics of the flat anisotropic models in the Lovelock gravity. I: The even-dimensional case
• On stable exponential solutions in Einstein-Gauss-Bonnet cosmology with zero variation of G
• Stable exponential cosmological solutions with zero variation of $G$ and three different Hubble-like parameters in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
• Cosmological solutions in Einstein-Gauss-Bonnet gravity with static curved extra dimensions
• Stable exponential cosmological solutions with zero variation of G in the Einstein-Gauss-Bonnet model with a Lambda-term
• Examples of stable exponential cosmological solutions with three factor spaces in EGB model with a $\Lambda$-term

Cited by in corpus (1)

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