In this paper we are looking for the exponential solutions (i.e. the solutions with the scale factors change exponentially over time) in the Einstein-Gauss-Bonnet gravity. We argue that we found all possible non-constant-volume solutions (up to permutations) in lower dimensions ((4+1) and (5+1)) and developed a scheme which allows one to find necessary conditions in arbitrary dimension.

In this paper we propose a scheme which allows one to find all possible exponential solutions of special class-non-constant volume solutions-in Lovelock gravity in arbitrary number of dimensions and with arbitrate combinations of Lovelock terms. We apply this scheme to (6 + 1)-and (7 + 1)-dimensional flat anisotropic cosmologies in Einstein-Gauss-Bonnet and third-order Lovelock gravity to demonstrate how our scheme does work. In course of this demonstration we derive all possible solutions in (6 + 1) and (7 + 1) dimensions and compare solutions and their abundance between cases with different Lovelock terms present. As a special but more "physical" case we consider spaces which allow three-dimensional isotropic subspace for they could be viewed as examples of compactification schemes. Our results suggest that the same solution with three-dimensional isotropic subspace is more "probable" to occur in the model with most possible Lovelock terms taken into account, which could be used as kind of anthropic argument for consideration of Lovelock and other higher-order gravity models in multidimensional cosmologies.

In this paper we investigate the constant volume exponential solutions (i.e. the solutions with the scale factors change exponentially over time so that the comoving volume remains the same) in the Einstein-Gauss-Bonnet gravity. We find conditions for these solutions to exist and show that they are compatible with any perfect fluid with the equation of state parameter ω < 1/3 if the matter density of the Universe exceeds some critical value. We write down some exact solutions which generalize ones found in our previous paper for models with a cosmological constant.

A D-dimensional Einstein-Gauss-Bonnet (EGB) flat cosmological model with a cosmological term Λ is considered. We focus on solutions with exponential dependence of scale factor on time. Using previously developed general analysis of stability of such solutions done by V.D.Ivashchuk (2016) we apply the criterion from that paper to all known exponential solutions upto dimensionality 7+1. We show that this criterion which guarantees stability of solution under consideration is fulfilled for all combination of coupling constant of the theory except for some discrete set.

We consider a particular example of dynamical compactification of an anisotropic 7+1 dimensional Universe in Einstein -Gauss -Bonnet gravity. Starting from rather general totally anisotropic initial conditions a Universe in question evolves towards a product of two isotropic subspaces. The first subspace expands isotropically, the second represents an "inner" isotropic subspace with stabilized size. The dynamical evolution does not require finetuning of initial conditions, though it is possible for a particular range of coupling constants. The corresponding condition have been found analytically and have been confirmed using numerical integration of equations of motion.

We consider numerically dynamics of a flat anisotropic Universe in Einstein-Gauss-Bonnet gravity with positive Λ in dimensionalities 5+1 and 6+1. We identify three possible outcomes of the evolution, one singular and two nonsingular. First nonsingular outcome is oscillatory. Second is the known exponential solution. The simplest version of it is the isotropic de Sitter solution. In Gauss-Bonnet cosmology there exist also anisotropic exponential solutions. When an exponential solution being an outcome of cosmological evolution has two different Hubble parameters, the evolution leads from initially totally anisotropic stage to a warped product of two isotropic subspaces. We show that such type of evolution is rather typical and possible even in the case when de Sitter solution also exists.

We consider dynamics of a flat anisotropic multidimensional cosmological model in Gauss-Bonnet gravity in the presence of a homogeneous magnetic field. In particular, we find conditions under which the known power-law vacuum solution can be an attractor for the case with non-zero magnetic field. We also describe a particular class of numerical solution in (5 + 1)-dimensional case which does not approach the power-law regime.

In this paper the dynamic compactification in Lovelock gravity with a cubic term is studied.The ansatz will be of space-time where the three dimensional space and the extra dimensions are constant curvature manifolds with independent scale factors. The numerical analysis shows that there exist a phenomenologically realistic compactification regime where the three dimensional hubble parameter and the extra dimensional scale factor tend to a constant. This result comes as surprise as in Einstein-Gauss-Bonnet gravity this regime exists only when the couplings of the theory are such that the theory does not admit a maximally symmetric solution (i.e. "geometric frustration"). In cubic Lovelock gravity however there always exists at least one maximally symmetric solution which makes it fundamentally different from the Einstein-Gauss-Bonnet case. Moreover, in opposition to Einstein-Gauss-Bonnet Gravity, it is also found that for some values of the couplings and initial conditions these compactification regimes can coexist with isotropizing solutions.