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Alexander B. Balakin

Publications and source records attributed to Alexander B. Balakin.

At least 19 recordsLinked to original sources
arXiv2026

Decay of a multi-axionic SU(N) symmetric color aether in the early Universe as an origin of emergence of a many-component dark matter

We establish a new SU(N) symmetric model of interaction between the fields of four types: the multiplet of vector fields, which describes the so-called color aether, the multiplet of pseudoscalar fields, which is associated with the multi-component cosmic dark matter, the gauge and gravitational fields. The extended Lagrangian of the model contains a new constructive element, which is based on the covariant SU(N) symmetric divergence of the multiplet of vector fields; this new element, being the multiplet of scalars from the point of view of spacetime transformations and the color vector from the point of view of the SU(N) group space, gives us the possibility to formulate properly the multi-axionic extension of the Peccei-Quinn theory. The hypothesis of a spontaneous polarization of the multi-axionic color aether in the early Universe is presented. The set of self-consistent master equations of the model is derived. An application to cosmology is considered: the obtained master equations are solved for the truncated test model based on the Bianchi-I spacetime platform.

gr-qc↗
arXiv2025

Extension of the Einstein-Dirac-axion-aether theory based on an effective metric with a spinor kernel

We consider an axionic extension of the Einstein-Dirac-aether theory, which is based on the spinor modification of the kinetic term of the pseudoscalar field and describes the backreaction of the spinor field on the axionic dark matter. The main instrument of this extension is the effective metric constructed using the aether velocity four-vector and a kernel, which depends on the basic spinor scalar and on the square of the basic spinor pseudoscalar. The periodic potential of the axion field includes a guiding function, which regulates the dynamics of axions and predetermines the properties of their equilibrium states. This guiding function and the kernel of the effective metric, as well, are considered to be functions of the expansion scalar of the aether flow. The master equation for the guiding function is obtained as a consequence of the Lagrangian invariance with respect to the discrete transformations prescribed by the axion field shift symmetry. The self-consistent set of coupled master equations is derived, which includes new source-terms in the modified master equations for the spinor, axion, vector and gravitational fields. Cosmological applications of the extended theory are considered; new exact solutions of these equations are presented for the isotropic homogeneous model of the Universe evolution. Discussion is focused on the mechanism of backreaction of the spinor field on the axionic dark matter evolution.

gr-qc↗
arXiv2025

Extended Einstein-Dirac-aether theory: Spinor modifications of the dynamic aether kinetic term

In the framework of the Einstein-Dirac-aether theory the extended model is established, in which the backreaction of the spinor field on the unit vector field, describing the dynamic aether, is taken into account. For this purpose, we extended the Jacobson constitutive tensor, which enters the kinetic part of the Lagrangian of the unit vector (aetheric) field, by the terms containing spinor tensors and pseudotensors. The self-consistent system of master equations for the unit vector field, as well as, the spinor and gravitational fields is derived using the variation formalism in the framework of the effective field theory up to the second order in derivatives.

gr-qc↗
arXiv2025

Kinetics of relativistic axionically active plasma in the field of dynamic aether. Part II: Particle dynamics and symptoms of plasma instability

In the paper [I], the first part of our work, we established the model of interaction of five elements: first, a unit time-like vector field, associated with the velocity of dynamic aether, second, the pseudoscalar field describing an axionic component of the dark matter, third, the electromagnetic field, fourth, the relativistic multi-component plasma and, fifth, the gravitational field. The initial step of analysis of this model was the reconstruction of the equilibrium states of the axionically-aetherically active plasma, which are characterized by frequent inter-particle collisions. In the second part of the work, presented here, in the framework of isotropic homogeneous cosmological model we consider the collisionless limit of the theory, and thus, we focus on the analysis of the particle dynamics under the influence of axionically-aetherically induced forces. The complete distribution functions, as exact solutions to the kinetic equations, are presented. Based on five examples of the background solutions of the model, we discuss the symptoms of plasma instability provoked by the influence of forces of the friction and tidal types.

gr-qc↗
arXiv2024

Kinetics of relativistic axionically active plasma in the field of dynamic aether. Part I: General formalism and new concept of equilibrium states

We establish an extended version of the kinetic theory of the relativistic axionically active multi-component plasma, which is based on the inclusion of a unit time-like vector field, associated with the velocity of dynamic aether, into the scheme of interactions. The proposed extension of the plasma theory can be indicated as semi-phenomenological. This term means that master equations for the gravitational, electromagnetic, pseudoscalar (axionic) and vector (aetheric) fields are derived using the Lagrange formalism, the kinetic equations for the distribution functions are obtained by the methods of the covariant statistics, however, the relativistic forces acting from the listed fields on the plasma particles are reconstructed phenomenologically based on classical analogies. We consider this work as a first part of a trilogy; here we presented, first, the complete formalism of this extended theory, second, the classification of forces, third, the new concept of equilibrium states in the relativistic axionically - aetherically active plasma.

gr-qc↗
arXiv2024

Isotropic cosmological model with aetherically active axionic dark matter

In the framework of the extended Einstein-aether-axion theory we study the model of a two-level aetheric control over the evolution of a spatially isotropic homogeneous Universe filled with axionic dark matter. Two guiding functions are introduced, which depend on the expansion scalar of the aether flow, equal to the tripled Hubble function. The guiding function of the first type enters the aetheric effective metric, which modifies the kinetic term of the axionic system; the guiding function of the second type predetermines the structure of the potential of the axion field. We obtained new exact solutions of the total set of master equations of the model (with and without cosmological constant), and studied in detail four analytically solvable submodels, for which both guiding functions are reconstructed and illustrations of their behavior are presented.

gr-qc↗
arXiv2023

The extended Einstein-Maxwell-aether-axion theory: Effective metric as an instrument of the aetheric control over the axion dynamics

In the framework of the Einstein-Maxwell-aether-axion theory we consider the self-consistent model based on the concept of a two-level control, which is carried out by the dynamic aether over the behavior of the axionically active electrodynamic system. The Lagrangian of this model contains two guiding functions, which depend on four differential invariants of the aether velocity: the scalar of expansion of the aether flow, the square of the acceleration four-vector, the squares of the shear and vorticity tensors. The guiding function of the first type is an element of the effective aetheric metric; this effective metric is involved in the formulation of kinetic terms for the vector, pseudoscalar and electromagnetic fields and predetermines features of their evolution. The guiding function of the second type is associated with the distribution of axions and describes its vacuum average value; basically, this function appears in the potential of the axion field and predetermines the position and depth of its minima. The self-consistent set of coupled master equations of the model is derived. The example of the static spherically symmetric system is considered as an application.

gr-qc↗
arXiv2023

Interaction of the Cosmic Dark Fluid with Dynamic Aether: Parametric Mechanism of Axion Generation in the Early Universe

We consider an isotropic homogeneous cosmological model with five interacting elements: first, the dynamic aether presented by a unit timelike vector field, second, the pseudoscalar field describing an axionic component of the dark matter, third, the cosmic dark energy, described by a rheologic fluid, fourth, the non-axionic dark matter coupled to the dark energy, fifth, the gravity field. We show that the early evolution of the Universe described by this model can include two specific epochs: the first one can be characterized as a super-inflation, the second epoch is associated with an oscillatory regime. The dynamic aether carries out a regulatory mission; the rheologic dark fluid provides the specific features of the spacetime evolution. The oscillations of the scale factor and of the Hubble function are shown to switch on the parametric (Floquet - type) mechanism of the axion number growth.

gr-qc↗
arXiv2023

Dynamic aether as a trigger for spontaneous spinorization in early Universe

In the framework of the Einstein-Dirac-aether theory we consider a phenomenological model of the spontaneous growth of the fermion number, which is triggered by the dynamic aether. The trigger version of spinorization of the early Universe is associated with two mechanisms: the first one is the aetheric regulation of behavior of the spinor field; the second mechanism can be related to a self-similarity of internal interactions in the spinor field. The dynamic aether is designed to switch on and switch off the self-similar mechanism of the spinor field evolution; from the mathematical point of view, the key of such a guidance is made of the scalar of expansion of the aether flow, proportional to the Hubble function in the isotropic cosmological model. Two phenomenological parameters of the presented model are shown to be considered as factors predetermining the total number of fermions born in the early Universe.

gr-qc↗
arXiv2023

Nonlinear interaction of the axion field with dynamic aether and SU(2) symmetric gauge field in the anisotropic Universe

Based on the concept of the dynamic aether emergence as a result of spontaneous polarization of the color aether, we consider the SU(2) symmetric theory of interaction of the gauge and axion fields in the framework of anisotropic cosmological model of the Bianchi-I type. We focus on the analysis of the non-Abelian analog of the U(1) symmetric model of axionically induced generation of the electric field in a magnetized medium.

gr-qc↗
arXiv2023

Axion electrodynamics on the Bianchi spacetime platform: Fingerprints of shear of the aether velocity

In the framework of axionically extended Einstein-Maxwell-aether theory we study the structure of the electromagnetic field allowed by the anisotropic cosmological spacetime platforms associated with the Bianchi models. These models guarantee that the aether velocity possesses the shear, and we focus on its role in the evolution of the axion-photon systems. In this short note we discuss the extended master equations obtained under the assumption that the square of the shear tensor is included in the potential of the axion field.

gr-qc↗
arXiv2023

Axionic extension of the Einstein-Dirac-aether theory: Degeneracy removal with respect to shear of the aether flow

We consider dynamics of the quartet of interacting cosmic substrata, which includes the dynamic aether, presented by the unit timelike vector field, the axionic dark matter, described by the pseudoscalar field, the spinor field associated with fermion particles, and the gravity field. The extended set of master equations is derived based on the idea that the potential of the axion field to be the function of seven arguments. The first one is, standardly, the pseudoscalar field; the second and third arguments are the fundamental spinor invariant and pseudoinvariant; the fourth and fifth ones are the aether-axion cross-invariants and cross-pseudoinvariants; the sixth argument is the expansion scalar, and the seventh one is the square of tensor of the shear of the aether flow. The complete set of master equations is derived and prepared for analysis.

gr-qc↗
arXiv2023

Nonlocal extension of relativistic non-equilibrium thermostatics

Based on the formalism of nonlocal extension of the Israel-Stewart causal thermodynamics on the one hand, and on the formalism of the extended thermostatics on the other hand, we propose the new model of nonlocal relativistic non-equilibrium thermostatics for description of the static spherically symmetric stellar systems. This nonlocal formalism operates with the pair of orthogonal four-vectors: one of them is the standard unit timelike medium velocity four-vector, the second one is the unit spacelike director. We derived the extended equation describing the profile of the non-equilibrium pressure, which can be indicated as the static analog of the Burgers constitutive equation known in classical rheology.

gr-qc↗
arXiv2022

Einstein-Yang-Mills-aether theory with nonlinear axion field: Decay of color aether and the axionic dark matter production

We establish a nonlinear version of the SU(N) symmetric theory, which describes self-consistently the interaction between the gravitational, gauge, vector and pseudoscalar (axion) fields. In the context of this theory the SU(N) symmetric multiplet of vector fields is associated with the color aether, the decay of which in the early Universe produced the canonic dynamic aether and the axionic dark matter. The SU(N) symmetric Yang-Mills field, associated with the color aether, forms the source, which transfers the energy of the decaying color aether to the axion field. The nonlinear modification of the model uses explicitly the requirement of discrete symmetry, prescribed by the axion field, and is based on the analogy with nonlinear physical pendulum. We show that in the framework of this nonlinear regular model the axion field can grow to an arbitrarily large value, thus explaining the abundance of the axionic dark matter in the Universe.

gr-qc↗
arXiv2022

Relativistic nonlinear axion magnetohydrodynamics

The new nonlinear axionically extended version of the general relativistic magnetohydrodynamics is formulated. The self-consistent formalism of this theory is based on the introduction into the Lagrangian of the new unified scalar invariant, which is quadratic in the Maxwell tensor, and contains two periodic functions of the pseudoscalar (axion) field. The constructed unified invariant and the elaborated nonlinear theory as a whole, are invariant with respect to two symmetries: first, the discrete symmetry associated with the properties of the axion field; second, the Jackson's SO(2) type symmetry intrinsic for the electromagnetism. The subsystem of the master equations, which describes the velocity four-vector of the hydrodynamic flow, is constructed in the framework of Eckart's theory of viscous heat-conducting fluid. The axionically extended nonlinear Faraday, Gauss and Ampere equations are supplemented by the ansatz about the large electric conductivity of the medium, which is usually associated with vanishing of the electric field. We have suggested two essentially new nonlinear models, in the framework of which the anomalous electric conductivity is being compensated by the appropriate behavior of the finite pseudoscalar (axion) field, providing the electric field in the magnetohydrodynamic flow to be finite (either to be proportional to the magnetic field, or to the angular velocity of the medium rotation)

hep-ph↗
arXiv2022

Self-interaction in a cosmic dark fluid: The four-kernel rheological extension of the equations of state

We establish a new self-consistent model of coupling between the cosmic dark energy and dark matter in the framework of the rheological approach, which is based on the representation of the equations of state in terms of integral operators of the Volterra-type. We elaborate the so-called four-kernel model, in the framework of which both the dark energy and dark matter pressures are presented by two integrals containing the energy densities of the dark energy and dark matter. For the Volterra operators, the kernels of which are associated with the effects of fading memory, the corresponding isotropic homogeneous cosmological model is shown to be exactly integrable. We consider the classification of the model exact solutions, based on the analysis of roots of the characteristic polynomial associated with the key equation of the presented model. The scalars of the pressure and energy-density of the dark energy and dark matter, the Hubble function and acceleration parameter are presented explicitly as the functions of the dimensionless scale factor. The scale factor as the function of the cosmological time is found in quadratures and is described analytically, qualitatively and numerically. Asymptotic analysis allowed us to classify the models with respect to behavior typical for the Big Rip, Little Rip and Pseudo Rip (de Sitter type). Two intriguing exact cosmological solutions are discussed, which describe the super-exponential expansion and the symmetric bounce. New solutions are presented, which correspond to the quasi-periodic behavior of the state functions of the dark fluid and of the geometric characteristics of the Universe.

gr-qc↗
arXiv2022

Nonlocal extension of causal thermodynamics of the isotropic cosmic fluid

We establish the nonlocal generalization of the Israel-Stewart model for the relativistic causal thermodynamics of the cosmic fluid, which evolves in the homogeneous isotropic Universe. Based on the second law of thermodynamics we derive the integro-differential master equation for the nonequilibrium pressure scalar and reduce it to the differential equation of the second order in time derivatives. We show that this master equation can be considered as the relativistic analog of the Burgers equation, which is known in the classical theory of viscoelasticity. We obtain the nonlinear key equation, which contains the energy density scalar only, and analyze two exact solutions of the model. The effective temperature is considered to be associated with the barotropic equation of state of the cosmic fluid.

gr-qc↗