Kinetics of small disturbances in an isotropic universe I. Derivation of the equations for the disturbances

Gravitational disturbances in an isotropic cosmological model are considered within the bounds of relativistic kinetic theory. It is assumed that the collision frequency of the particles of the medium is much smaller than the frequency of the disturbances being studied. Equations are obtained for scalar, vector, and tensor disturbances in the case where the undisturbed solution describes a flat, isotropic cosmological model.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 30–35, March, 1978.     

Kinetics of small perturbations in an isotropic world

Long-wavelength gravitational perturbations are studied in an isotropic expanding universe filled with an ultrarelativistic gas. A kinetic study in the collisionless approximation shows that scalar and vector perturbations which appear at a time ₀ 1/n, where N is the wave vector and is the time coordinate x⁴, grow if the perturbation of the macroscopic momentum density of the gas at time ₀ is nonvanishing. The growth continues until the time ₁=27₀, at which the perturbation of the macroscopic momentum density of the gas vanishes. A solution is also derived for tensor perturbations in the limit n 1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 37–45, April, 1978.     

Relativistic collisionless gas in an isotropic universe within the framework of the Einstein-Cartan theory

Exact solutions of the self-consistent system-of Einstein-Cartan-Vlasov equations in nonrelativistic and ultrarelativistic limits are obtained for a spinless collisionless gas. The investigation is performed for different irreducible parts of the torsion tensor and different values of the cosmological constant. It is shown that torsion creates a curvature type effect. The solution is singular for t = 0. It is shown that the asymptotic of the scale factor a() in the ultrarelativistic limit for the torsion expressed in terms of its trace can differ from the Friedman one.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 62–67, June, 1989.The author is grateful to G. G. Ivanov and A. V. Zakharov for a number of valuable remarks, and to Prof. V. N. Ponomarev for discussing the research and for critical remarks.     

The propagation of infinitesimal disturbances in an ultrarelativistic gas according to the method of elementary solutions

It has recently been shown that a linearized relativistic BGK model can be reduced, in the ultrarelativistic limit, to a system of three uncoupled transport equations for thermal, sound, and shear waves. The equation describing the propagation of thermal waves is the well-known one-speed neutron transport with isotropic scattering in the conservative case. In this paper the solution of the half-space problem for the equation describing the propagation of shear and sound waves is given according to Case's elementary solutions method.     

Statistical description of an ensemble of ultrarelativistic particles in a spatially flat universe

The kinetic equation for massless particles in an unperturbed Friedman universe with gravitational interactions taken into account is obtained by averaging the collisionless kinetic equations over local background gravitational field fluctuations. Uniformly distributed spherically symmetric fluctuations of an ultrarelativistic fluid serve as local inhomogeneities in a spatially flat universe. It is shown that the collision integral of our kinetic equation does not vanish when the distribution function is homogeneous and isotropic.     

Generation of longitudinal plasma oscillations by gravitational perturbations in an isotropic universe

The electric charge density induced by scalar gravitational perturbations in the lepton and radiation-dominated stages of the expansion of the universe is calculated. It is shown that the formation of clusters of matter is accompanied in the radiation-dominated stage by a build-up of positive charge in the central regions of the cluster. The charge-mass relation of the clusters is calculated.Translated from Izvestiya Vysshkikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 52–57, May, 1986.     

Propagation of transverse electromagnetic waves with gravitational perturbations in an isotropic universe

The combined behavior of gravitational and electromagnetic perturbations in the radiation-dominated plasma of an isotropic universe is considered. It is shown that transverse electromagnetic waves and vector and tensor gravitational perturbations are independent of one another. The propagation of transverse electromagnetic waves during the lepton and radiation-dominated phases is determined. It is shown that the gravitational perturbations help to excite longitudinal electromagnetic fields in the radiation-dominated plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–54, December, 1985.     

Perfect fluid in a static isotropic universe

Solutions of the Einstein field equations for a perfect fluid in a static isotropic gravitational field are obtained. The solution given by Melnick and Tavensky is corrected.     

Solution of a linearized kinetic model for an ultrarelativistic gas

A linearized model of the Boltzmann equation for a relativistic gas is shown to be reducible, in the ultrarelativistic limit and for (1 + 1)-dimensional problems, to a system of three uncoupled transport equations, one of which is well known. A general method for solving these equations is recalled, with a few new details, and applied to the solution of two boundary value problems. The first of these describes the propagation of an impulsive change in a half space and is shown to give an explicit example of the recently proved result that no signal can propagate with speed larger than the speed of light, according to the relativistic Boltzmann equation. The second problem deals with steady oscillations in a half space and illustrates the meaning of certain recent results concerning the dispersion relation for linear waves in relativistic gas.     

On isotropic turbulence in the dark fluid universe

As a first part of this work, experimental information about the decay of isotropic turbulence in ordinary hydrodynamics, [`(u²(t))] μ t^-6/5\overline{\mathbf{u}^{2}(t)}\propto t^{-6/5}, is used as input in FRW equations in order to investigate how an initial fraction f of turbulent kinetic energy in the cosmic fluid influences the cosmological development in the late, quintessence/phantom, universe. First order perturbative theory to the first order in f is employed. It turns out that both in the Hubble factor and in the energy density, the influence from the turbulence fades away at late times. The divergences in these quantities near the Big Rip behave essentially as in a non-turbulent fluid. However, for the scale factor, the turbulence modification turns out to diverge logarithmically. As a second part of our work, we consider the full FRW equation in which the turbulent part of the dark energy is accounted for by a separate term. It is demonstrated that turbulence occurrence may change the future universe evolution due to dissipation of dark energy. For instance, the phantom-dominated universe becomes asymptotically a de Sitter one in the future, thus avoiding the Big Rip singularity.     

The kinetic theory of the perturbations in the isotropic universe

The short wave and long wave gravitational perturbations in the isotropic universe are considered by using the general relativistic kinetic theory. It is shown that the short wave perturbations propagate in the ultrarelativistic collisionless gas with the velocity of light.     

Numerical evolution,linear and nonlinear,of spherically symmetric deviations from an isotropic universe

We describe an algorithm for solving 1 + 1-systems that are in symmetric hyperbolic form. It is applied to spherically symmetric deviations from ak = 0, radiation filled Isotropic universe. We compare the solution to the full Einstein equations with those of the linearized equations. For small enough initial data the evolutions are indistinguishable. However, for large data, i.e., for initial density contrasts in the 1 percent range, trapped surfaces appear and singularities form.     

Stability of equilibrium orbits in isochronous ultrarelativistic cyclotron II

The paper investigates the stability of equilibrium orbits of charged particles in one variant of the ultrarelativistic cyclotron. The Bogoljubov-Krylov method of averaging is used to show that one of the pairs of principal equilibrium orbits, which were found in the first part of the paper, is stable while the second is unstable. The stability limit is identical with the limit of the existence of equilibrium orbits. The dependence of the frequencies of betatron oscillations on the field parameters is shown in the stability diagrams. Brief mention is made of the magnet of the variant of an ultrarelativistic cyclotron with axially scalloped equilibrium orbit.     

Consistency of Pantheon+ supernovae with a large-scale isotropic universe

We investigate the possible anisotropy of the universe using data on the most up-to-date type Ⅰa supernovae,i.e., the Pantheon+compilation.We fit the full Pantheon+data with the dipole-modulated ΛCDM model and find that the data are well consistent with a null dipole.We further divide the full sample into several sub samples with different high-redshift cutoffs z_c.It is shown that the dipole appears at the 2σ confidence level only if z_c≤0.1,and in this redshift region,the d...     

A dynamic model of spherical perturbations in the Friedmann Universe. II. Retarded solutions to an ultrarelativistic equation of state

The exact linear retarded spherically symmetrical solutions to the Einstein equations linearized around the Friedmann background are derived and examined for an ultrarelativistic equation of state. The uniqueness of the solutions in class C¹ is proved. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 69–76, July, 2008.     

Quantum dynamics of an isotropic cosmological model with relativistic gas

A canonical time parameter corresponding to the synchronous reference frame is found for an isotropic cosmological model with relativistic gas. Canonical quantization of the model is performed. In the quantum theory, the radius of the Universe is an operator-valued function of time, whose values at different moments of time commute among themselves, and the state of the Universe itself does not change with time. In particular, this means that in experiments in which the radius of the Universe is measured, the presence of singularity is unavoidable within a finite interval of time in the past, and, for closed models, in the future.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 9–14, July, 1990.The authors thank L. D. Faddeev for his interest to their work, and V. A. Franke for stimulating discussions.     

Regularization of the fermion stress-energy tensor in isotropic models of the universe

Regularization of the stress-energy tensor of fermions created in isotropic cosmological models, equivalent to renormalization of the gravitational constant is performed. Energy density and pressure of created pairs are calculated for various stages of evolution and various expansion laws.     

Kinetics of ions in a neutral gas upon abrupt application of an electric field. II: Various models of interaction

A new method for calculating the matrix elements of the collision integral in the Boltzmann equation is used for studying the behavior of an ion impurity upon an abrupt application of an electric field. For five models of interaction, the behavior of mobility is analyzed and the evolution of the distribution function for various values of the electric field is illustrated. The initial stage of runaway of ions is studied in the case of the Coulomb interaction. Two methods for improving the convergence of the polynomial expansions of the distribution function are considered.     

Dielectric constant of an ultrarelativistic plasma

An analytic expression is derived for the longitudinal dielectric constant _l of an isotropic collisionless high-temperature plasma which is valid for the entire range of phase velocities in which there is no Landau damping or it is exponentially small. This expression contains the formulas for _l given in the papers of Silin and Mikhailovskii as limiting cases. Numerical calculations for the temperatures 10 mc² and 100 mc² are illustrated graphically.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 57–60, September, 1982.