Linear perturbations on the cosmological background in the relativistic theory of gravitation: II. Appendix

We have solved the general equations derived in Part I [1] to describe the evolution of the gravitational instability on the background of an oscillating, homogeneous, and isotropic universe in the relativistic theory of gravitation considering a massive graviton. Complete solutions, along with their short-wave and long-wave asymptotics, are given for most distinctive stages of the evolution of the universe, namely, near the turning points corresponding to the maximum and minimum densities, as well as in the radiation-dominated, nonrelativistic, and quintessence stages. In all these cases, except for the turning points, the gauge vectors have been determined for the scalar and vector perturbations, allowing the elimination of wave solutions with a phase velocity that is equal to the speed of light. We conclude that, in principle, the observed structure of the universe could have been formed during a sufficiently large number of its cycles.     

Bimetric gravitation theory on a cosmological basis

In the bimetric theory of gravitation the background metric tensor , previously taken as describing flat space-time, is now chosen on the basis of a model of the universe. In accordance with the perfect cosmological principle, it is taken as describing a space-time of constant curvature. There are three possible forms, corresponding tok=0, 1, –1. Only fork=1 (a closed universe) does the model not go through a singular state; hence this is the appropriate choice. The isotropic solution of the field equations can be chosen to agree with the present cosmological observations. For small systems like the solar system the theory gives the same results as before, in agreement with those of general relativity.     

Some cosmological models in the bimetric theory of gravitation

It is shown that the field equations of the bimetric theory of gravitation have solutions corresponding to a class of homogeneous isotropic cosmological models with negative spatial curvature (k=–1). Some examples are given.     

Magnetized cosmological models in bimetric theory of gravitation

Bianchi type-III magnetized cosmological model when the field of gravitation is governed by either a perfect fluid or cosmic string is investigated in Rosen’s [1] bimetric theory of gravitation. To complete determinate solution, the condition, viz., A=(BC) ⁿ , where n is a constant, between the metric potentials is used. We have assumed different equations of state for cosmic string [2] for the complete solution of the model. Some physical and geometrical properties of the exhibited model are discussed and studied.     

New energy-momentum tensor in relativistic gravitation theory

Expressions for a new canonical energy-momentum tensor and an internal angular momentum of the gravitational field are derived in the context of bimetric relativistic gravitation theory based on the variational principle. A system of relations for the determining parameters of the gravitational field and matter involving, in particular, the continuity condition for the energy-momentum flux density is formulated on the discontinuity surface. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 52–58, April, 2006.     

The causality principle in relativistic gravitation theory

It is shown that relativistic gravitation theory is consistent with the existence of vacuum-like medium. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 20–25, April, 2007.     

General relativistic theory of gravitation exhibiting complete group covariance

The geometry of the group manifold is generalized to allow the construction of a general relativistic theory exhibiting all the degrees of freedom of the group in its dynamical variables. The theory has features of a multidimensional Kaluza-Klein theory with noncommuting Killing vectors. The resulting fields suggest, however, a teleparallelistic formulation. The geometry and gauge invariance of the theory are discussed.     

The cosmological principle and a generalization of Newton's theory of gravitation

Using the notion of Galilei manifolds a geometric formulation of the cosmological principle for the prerelativistic theory of gravitation is presented. This is applied to a generalization of the Newton-Cartan theory which admits solutions with a curved Galilei structure. Furthermore, the limit relation between this theory and some relativistic theories is discussed.     

Homogeneous isotropic cosmological model of space-time with torsion in the Einstein-Cartan theory of gravitation

A systematic treatment is applied to the cosmological problem in the Einstein-Cartan theory of gravitation on the basis of the variational principle formulated previously for an ideal fluid in space with torsion. Exact solutions are obtained for homogeneous isotropic cosmological models with flat three-dimensional space filled with powdery matter and a fluid with an equation of state p=/3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 24–28, March, 1977.The author thanks Professor D. D. Ivanenko and members of the seminar conducted by him for useful discussions.     

Phenomenological formulation of direct interparticle interaction in relativistic theory of gravitation

The general equations of relativistic dynamics of point masses in the post-Newtonian approximation and in the approximation of ultrarelativistic velocities are considered. The consequences of the weak principle of equivalence and its relation with the hypothesis of geodesics is studied. It is shown that, in the above approximations, the equations of motion reduce to the equations of Riemann geodesics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 69–73, November, 1986.The authors thank K. A. Piragas for his attention to the study and R. P. Gaida, Yu. B. Klyuchkovskii, and V. I. Tret'yak for useful discussions.