Narrow Results

In the paper, multidimensional anisotropic metric and density of vacuum energy in the Kasner's model are investigated. It is shown that the presence of scalar field in model is equivalent to metric in the spacetime with additional dimensions and we propose the idea of generating additional dimensions by massless scalar field. We propose a method of renormalization of metric that describes conversion from spacetime with scalar field to higher-dimensional spacetime. We obtain the expression for cosmological constant which depends on the initial conditions for anisotropic metric coefficients. Using the method of Bogolubov, we investigate the influence of anisotropic metric onto the cosmological birth of particles and obtain the effective mass of scalar field depending on the cosmological constant.

We consider a magnetized degenerate gas of fermions as the matter source of a homogeneous but anisotropic Bianchi I space–time with a Kasner-like metric. We examine the dynamics of this system by means of a qualitative and numerical study of Einstein–Maxwell field equations which reduce to a non-linear autonomous system. For all initial conditions and combinations of free parameters, the gas evolves from an initial anisotropic singularity into an asymptotic state that is completely determined by a stable attractor. Depending on the initial conditions the anisotropic singularity is of the "cigar" or "plate" types.

The curved spacetime Maxwell equations are applied to the anisotropically expanding Kasner metrics. Using the application of vector identities we derive second-order differential wave equations for the electromagnetic field components; through this explicit derivation, we find that the second-order wave equations are not uncoupled for the various components (as previously assumed), but that gravitationally induced coupling between the electric and magnetic field components is generated directly by the anisotropy of the expansion. The lack of such coupling terms in the wave equations from several prior studies may indicate a generally incomplete understanding of the evolution of electromagnetic energy in anisotropic cosmologies. Uncoupling the field components requires the derivation of a fourth-order wave equation, which we obtain for Kasner-like metrics with generalized expansion/contraction rate indices. For the axisymmetric Kasner case, $(p_1,p_2,p_3)=(1,0,0)$, we obtain exact field solutions (for general propagation wave vectors), half of which appear not to have been found before in previous studies. For the other axisymmetric Kasner case, $\{p_1,p_2,p_3\}=\{(-1/3),(2/3),(2/3)\}$, we use numerical methods to demonstrate the explicit violation of the geometric optics approximation at early times, showing the physical phase velocity of the wave to be inhibited towards the initial singularity, with $v\to 0$ as $t\to 0$.

The gravitational interaction is expected to be modified for very short distances. This is particularly important in situations in which the curvature of spacetime is large in general, such as close to the initial cosmological singularity. The gravitational dynamics is then captured by the higher curvature terms in the action, making it difficult to reliably extrapolate any prediction of general relativity. In this note we review pure Lovelock equations for Kasner-type metrics. These equations correspond to a single Nth order Lovelock term in the action in d = 2N + 1, 2N + 2 dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. These are classified in several isotropy types. Some of these families correspond to degenerate classes of solutions, such that their dynamics is not completely determined by the equations of pure Lovelock gravity. Instead, these Kasner solutions become sensitive to the subleading terms in the Lovelock series.