Axionic extension of the Einstein-aether theory

We extend the Einstein-aether theory to take into account the interaction between a pseudoscalar field, which describes the axionic dark matter, and a time-like dynamic unit vector field, which characterizes the velocity of the aether motion. The Lagrangian of the Einstein-aether-axion theory includes cross-terms based on the axion field and its gradient four-vector, on the covariant derivative of the aether velocity four-vector, and on the Riemann tensor and its convolutions. We follow the principles of the Effective Field theory, and include into the Lagrangian of interactions all possible terms up to the second order in the covariant derivative. Interpretation of new couplings is given in terms of irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. A spatially isotropic and homogeneous cosmological model with dynamic unit vector field and axionic dark matter is considered as an application of the established theory; new exact solutions are discussed, which describe models with a Big Rip, Pseudo Rip and de Sitter-type asymptotic behavior.Comment: 15 pages, 0 figures, accepted for publication in Physical Review

Curvature Coupling and Accelerated Expansion of the Universe

A new exactly solvable model for the evolution of relativistic kinetic system interacting with an internal stochastic reservoir under the influence of a gravitational background expansion is established. This model of self-interaction is based on the relativistic kinetic equation for the distribution function defined in the extended phase space. The supplementary degree of freedom is described by the scalar stochastic variable (Langevin source), which is considered to be the constructive element of the effective one-particle force. The expansion of the Universe is shown to be accelerated for the suitable choice of the non-minimal self-interaction force.Comment: 12 pages, no figure

Electrodynamics of a Cosmic Dark Fluid

Cosmic Dark Fluid is considered as a non-stationary medium, in which electromagnetic waves propagate, and magneto-electric field structures emerge and evolve. A medium - type representation of the Dark Fluid allows us to involve into analysis the concepts and mathematical formalism elaborated in the framework of classical covariant electrodynamics of continua, and to distinguish dark analogs of well-known medium-effects, such as optical activity, pyro-electricity, piezo-magnetism, electro- and magneto-striction and dynamo-optical activity. The Dark Fluid is assumed to be formed by a duet of a Dark Matter (a pseudoscalar axionic constituent) and Dark Energy (a scalar element); respectively, we distinguish electrodynamic effects induced by these two constituents of the Dark Fluid. The review contains discussions of ten models, which describe electrodynamic effects induced by Dark Matter and/or Dark Energy. The models are accompanied by examples of exact solutions to the master equations, correspondingly extended; applications are considered for cosmology and space-times with spherical and pp-wave symmetries. In these applications we focused the attention on three main electromagnetic phenomena induced by the Dark Fluid: first, emergence of Longitudinal Magneto-Electric Clusters; second, generation of anomalous electromagnetic responses; third, formation of Dark Epochs in the Universe history.Comment: 39 pages, 0 figures, replaced by the version published in MDPI Journal "Symmetry" (Special Issue: Symmetry: Feature Papers 2016); typos correcte

Einstein-aether theory: Dynamics of relativistic particles with spin or polarization in a G\"odel-type universe

In the framework of the Einstein-aether theory we consider a cosmological model, which describes the evolution of the unit dynamic vector field with activated rotational degree of freedom. We discuss exact solutions of the Einstein-aether theory, for which the space-time is of the G\"odel-type, the velocity four-vector of the aether motion is characterized by a non-vanishing vorticity, thus the rotational vectorial modes can be associated with the source of the universe rotation. The main goal of our paper is to study the motion of test relativistic particles with vectorial internal degree of freedom (spin or polarization), which is coupled to the unit dynamic vector field. The particles are considered as the test ones in the given space-time background of the G\"odel-type; the spin (polarization) coupling to the unit dynamic vector field is modeled using exact solutions of three types. The first exact solution describes the aether with arbitrary Jacobson's coupling constants; the second one relates to the case, when the Jacobson's constant responsible for the vorticity is vanishing; the third exact solution is obtained using three constraints for the coupling constants. The analysis of the exact expressions, which are obtained for the particle momentum and for the spin (polarization) four-vector components, shows that the interaction of the spin (polarization) with the unit vector field induces a rotation, which is additional to the geodesic precession of the spin (polarization) associated with the universe rotation as a whole.Comment: 15 page

Thermodynamic equilibrium in the expanding universe

We show that a relativistic gas may be at ``global'' equilibrium in the expanding universe for any equation of state $0 < p \leq \rho /3$, provided that the gas particles move under the influence of a self-interacting, effective one-particle force in between elastic binary collisions. In the force-free limit we recover the equilibrium conditions for ultrarelativistic matter which imply the existence of a conformal timelike Killing vector.Comment: 10 pages, Latex, to appear in GR

Inflation in a self-interacting gas universe

We show that a de Sitter spacetime is a solution of Einstein's field equations with the energy momentum tensor of a self-interacting, classical Maxwell-Boltzmann gas in collisional equilibrium. The self-interaction is described by a four-force which is quadratic in the (spatially projected) particle four-momenta. This force does not preserve the particle number and gives rise to an exponential increase in the comoving entropy of the universe while the temperature of the latter remains constant. These properties of a gas universe are related to the existence of a ``projector-conformal'' timelike Killing vector representing a symmetry which is ``in between'' the symmetries characterized by a Killing vector and those characterized by a conformal Killing vector.Comment: 10 pages, Revtex, Journal reference: Phys.Rev.D58 063503 (1998

Self-interacting gas in a gravitational wave field

We investigate a relativistic self-interacting gas in the field of an external {\it pp} gravitational wave. Based on symmetry considerations we ask for those forces which are able to compensate the imprint of the gravitational wave on the macroscopic 4-acceleration of the gaseous fluid. We establish an exactly solvable toy model according to which the stationary states which characterize such a situation have negative entropy production and are accompanied by instabilities of the microscopic particle motion. These features are similar to those which one encounters in phenomena of self-organization in many-particle systems.Comment: 17 pages, to be published in the GRG-Journa