Dynamics of the cosmological models with perfect fluid in Einstein-Gauss-Bonnet gravity: low-dimensional case

In this paper we performed investigation of the spatially-flat cosmological models whose spatial section is product of three- ("our Universe") and extra-dimensional parts. The matter source chosen to be the perfect fluid which exists in the entire space. We described all physically sensible cases for the entire range of possible initial conditions and parameters as well as brought the connections with vacuum and $\Lambda$-term regimes described earlier. In the present paper we limit ourselves with $D=1, 2$ (number of extra dimensions). The results suggest that in $D=1$ there are no realistic compactification regimes while in $D=2$ there is if $\alpha > 0$ (the Gauss-Bonnet coupling) and the equation of state $\omega < 1/3$, the measure of the initial conditions leading to this regime is increasing with growth of $\omega$ and reaches its maximum at $\omega \to 1/3 - 0$. We also describe some pecularities of the model, distinct to the vacuum and $\Lambda$-term cases -- existence of the isotropic power-law regime, different role of the constant-volume solution and the presence of the maximal density for $D = 2$, $\alpha < 0$ subcase and associated features.Comment: 35 pages, 9 figure

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

We investigate possible regimes in spatially flat vacuum cosmological models in cubic Lovelock gravity. The spatial section is a product of three- and extra-dimensional isotropic subspaces. This is the second paper of the series and we consider D=5 and general D>=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 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 for D>=3 there are regimes with realistic compactification originating from `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>=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: $\alpha > 0$, $\beta < 0$, $\mu \leqslant \mu_4$ and entire $\alpha > 0$, $\beta > 0$. Let us note that for D>=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>=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 low-energy one with realistic compactification.Comment: 34 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1804.0693

The dynamics of the flat anisotropic models in the Lovelock gravity. I: The even-dimensional case

In this article we give a full description of the dynamics of the flat anisotropic (4+1)-dimensional cosmological model in the presence of both Gauss-Bonnet and Einstein contributions. This is the first complete description of this model with both terms taken into account. Our data is obtained using the numerical analysis, though, we use analytics to explain some features of the results obtained, and the same analytics could be applied to higher-dimensional models in higher-order Lovelock corrections. Firstly, we investigate the vacuum model and give a description of all regimes; then, we add a matter source in the form of perfect fluid and study the influence the matter exerts upon the dynamics. Thus, we give a description of matter regimes as well. Additionally, we demonstrate that the presence of matter not only "improves" the situation with a smooth transition between the standard singularity and the Kasner regime, but also brings additional regimes and even partially "erases" the boundaries between different regimes inside the same triplet. Finally, we discuss the numerical and analytical results obtained and their generalization to the higher-order models.Comment: 20 pages, 7 figures; v2 - minor corrections, references adde