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.
Highlights
It is not widely known but the idea of extra dimensions is older general relativity (GR) itself
Page 3 of 19 611 or are they just solutions with no connection to the reality? To answer this question, we have considered the cosmological model in Einstein–Gauss– Bonnet (EGB) gravity with the spatial part being the product of three- and extra dimensional parts with both subspaces being spatially flat
That we expect that the dynamics of the -term cubic Lovelock gravity to be even more interesting and we are going to consider this case shortly. This concludes our study of the cosmological models in vacuum cubic Lovelock gravity
Summary
It is not widely known but the idea of extra dimensions is older general relativity (GR) itself. In [56] we demonstrated the there exist the phenomenologically sensible regime when the curvature of the extra dimensions is negative and the EGB theory does not admit a maximally-symmetric solution In this case both the three-dimensional Hubble parameter and the extradimensional scale factor asymptotically tend to the constant values. We have considered the cosmological model in EGB gravity with the spatial part being the product of three- and extra dimensional parts with both subspaces being spatially flat As both subspaces are spatially flat, we can rewrite the equations of motion in terms of Hubble parameters, so that they become first order differential equations and could be analytically analyzed to find all possible regimes, asymptotes, exponential and power-law solutions. We draw conclusions and formulate perspective directions for further investigations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
