41 research outputs found

### Realistic Compactification Models in Einstein-Gauss-Bonnet Gravity

We report the results of a study on the dynamical compactification of
spatially flat cosmological models in Einstein-Gauss-Bonnet gravity. The
analysis was performed in the arbitrary dimension in order to be more general.
We consider both vacuum and $\Lambda$-term cases. Our results suggest that for
vacuum case, realistic compactification into the Kasner (power law) regime
occurs with any number of dimensions ($D$), while the compactification into the
exponential solution occurs only for $D \geqslant 2$. For the $\Lambda$-term
case only compactification into the exponential solution exists, and it only
occurs for $D \geqslant 2$ as well. Our results, combined with the bounds on
Gauss-Bonnet coupling and the $\Lambda$-term ($\alpha, \Lambda$, respectively)
from other considerations, allow for the tightening of the existing constraints
and forbid $\alpha < 0$.Comment: 21 pages, 9 figures, published in Particles in the Special Issue
Selected Papers from "The Modern Physics of Compact Stars and Relativistic
Gravity 2017

### 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

### 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

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

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 $D
\geqslant 3$ 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 $D
\geqslant 3$. 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 $D \geqslant 3$ are different. Combining the two
described affects allows us to construct a scenario in $D \geqslant 3$, where
isotropisation of outer and inner subspaces is reached dynamically from rather
general anisotropic initial conditions.Comment: 22 pages, 3 figure