Cosmological Scalar in the Jordan-Brans-Dicke Theory. I

A variant of the Jordan-Brans-Dicke (JBD) theory is examined which contains a cosmological scalar that is written so that on going to the Einstein representation it becomes the ordinary cosmological constant of general relativity theory. This paper is divided into two parts. In Part I we examine the cosmological solutions for the Einstein representation of the JBD theory, i.e., in the presence of a minimally coupled scalar field. In Part II we shall study the cosmological solutions in the proper representation of the JBD theory with a self consistent scalar field. The analysis of these solutions is of interest in connection with modern concepts of the evolution of the universe, in particular, with the observed acceleration of cosmological expansion and estimates of the density of dark matter and dark energy.__________Translated from Astrofizika, Vol. 48, No. 3, pp. 455–462 (August 2005).     

The Cosmological Scalar in the Jordan-Brans-Dicke Theory. II.

Cosmological solutions are examined in the proper representation of the JBD theory with a dominant nonminimally coupled scalar field. It is shown that only the introduction of a cosmological scalar that transforms to the ordinary cosmological constant in the Einstein representation enables a phase of evolution with a uniform and then an accelerated expansion of the universe over cosmological time scales. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 633–640 (November 2005).     

Exact self-similar Bianchi II solutions for some scalar-tensor theories

We study how may behave the gravitational and the cosmological “constants”, (G and Λ) in several scalar-tensor theories with Bianchi II symmetries. By working under the hypothesis of self-similarity we find exact solutions for three different theoretical models, which are: the Jordan-Brans-Dicke (JBD) with Λ(?), the usual JBD model with potential U(?) (that mimics the behavior of Λ(?)) and the induced gravity (IG) model proposed by Sakharov and Zee. After a careful study of the obtained solutions we may conclude that the solutions are quite similar although the IG model shows some peculiarities.     

The deviation of light path in Einstein–Brans–Dicke theory

Both Jordan–Brans–Dicke (shortened JBD) theory and Brans–Dicke theory in the Einstein’s frame (shortened EBD) are treated as Brans–Dicke theory. However, we learn that only Pauli metric represents the massless spin-two graviton and thus, should be identified as physical. If one just considers the weak field approximation and Newtonian limit, EBD theory gives the same results with Einstein’s general relativity. So, it is necessary to consider strong field effects and cosmological model. The purpose of this paper is to find the exact spherically symmetric metric in the strong field situation, and deduce the deviation of light path in EBD theory.     

On string cosmology with loop corrections

Homogeneous cosmological models are investigated within the framework of low- energy string gravitation with loop corrections. Various conformai representations of the effective action are considered. Without specifying the correction functions in the Lagrangian, cosmological solutions are found with an arbitrary curvature and with dilaton fields, moduli fields, and Kalb- Ramond fields corresponding to a source with an extremely stiff equation of state. They generalize previously known solutions of the tree approximation. The behavior of the solutions in different asymptotic domains is investigated. Translated from Astrofizika, Vol. 41, No. 2, pp. 277–295, April-June, 1998.     

Self-similar chameleon Jordan-Brans-Dicke cosmological models

In this paper we study the chameleon Jordan-Brans-Dicke (JBD) cosmological models under the hypothesis of self-similarity. Since there are several ways to define the matter Lagrangian for a perfect fluid: L _m =?ρ and L _m =γρ, we show that they bring us to obtain two completely different cosmological models. In the first approach, L _m =?ρ, there is ordinary matter conservation, while in the second approach, L _m =γρ, we get matter creation processes. We deduce for each approach the behaviour of each physical quantity, under the self-similar hypothesis, by employing the Lie group method. The results are quite general and valid for any homogeneous geometry (FRW, Bianchi types, etc.). As example, we calculate exact solutions for each approach by considering the case of a Bianchi II geometry. In this way we can determine the exact behaviour of each physical quantity and in particular of G _eff and U (the potential that mimics the cosmological constant).We compare the solutions with the obtained ones in the framework of the usual JBD models.     

Group-theoretical description of radiative transfer in one-dimensional media

Group theory is used to describe a procedure for adding inhomogeneous absorbing and scattering atmospheres in a one-dimensional approximation. The inhomogeneity originates in the variation of the scattering coefficient with depth. Group representations are derived for the composition of media in three different cases: inhomogeneous atmospheres in which the scattering coefficient varies continuously with depth, composite or multicomponent atmospheres, and the special case of homogeneous atmospheres. We extend an earlier proposal to solve problems in radiative transfer theory by first finding global characteristics of a medium (reflection and transmission coefficients) and then determining the internal radiation field for an entire family of media without solving any new equations. Semi-infinite atmospheres are examined separately. For some special depth dependences of the scattering coefficients it is possible to obtain simple analytic solutions expressed in terms of elementary functions. An algorithm for numerical solution of radiative transfer problems in inhomogeneous atmospheres is described.     

A class of new Bianchi I perfect fluid space-times

A procedure to generate new exact solutions to Einstein equations for perfect fluids is applied to LRS Bianchi type I line-element. Starting from some known solutions a class of new perfect fluid solutions of Bianchi type I are presented. The physical and kinematical properties of spatially homogeneous and anisotropic cosmological models are studied.     

Symbolic analytical developments of the zero pressure cosmological model of the universe

In the present paper, literal analytical solutions in power series forms are developed for the radius of curvature and the expansion velocity of the zero pressure cosmological models of the universe at any time t. Also, we develop literal analytical solutions in power series forms for the inverse problem of the zero pressure cosmological model, that is to find the time $t=\tilde{t}$ (say) at which the radius of curvature of the model $R=\tilde{R}$ (say) is known. The importance of these analytical power series representations is that, they are invariant under many operations because, addition, multiplication, exponent ion, integration, different ion, etc of a power series is also a power series. A fact which provides excellent flexibility in dealing with analytical as well as computational developments of the problems related to zero pressure cosmological models.For computational developments of these solutions, an efficient method using continued fraction theory is provided. By means of the present methods we able to analyze some known zero-pressure cosmological models, of these are Einstein and De Sitter models. In addition we also analyzed some other models by which one can know if the universe keep expanding forever, or will it reach a maximal size and then turn into contraction stage.     

Analytical theories of satellite motion constructed with a new package of formula manipulation and compared with numerical integration

Specialized to the Lie series based perturbation method of Kirchgraber and Stiefel (1978) a new computer algebra package called ANALYTOS has been developed for constructing analytical orbital theories either in noncanonical or canonical form. We present results on the (extended) Main Problem of orbital theory of artificial earth satellites and related issues. The order of the solutions achieved is generally one order higher than those known from literature. Moreover, the analytical orbits have been checked succesfully against precise numerical ephemerides. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analytic continuation of quasi-periodic orbits from non-linear periodic modes

A new theory is formulated for the analytic continuation of quasi-periodic orbits from non-linear, periodic modes of a two degree-of-freedom system in rotating coordinates. Formal solutions of the equations of motion are developed in series expansions, with the non-linear modes as reference solutions. Conditions are determined on the existence and boundedness of the time-dependent coefficients of the velocity field. Boundedness properties of the orbits are specified by an orbit function derived from the Jacobi integral.     

A note on vacuum self-creation cosmological models

The vacuum field equations of the self-creation theory of gravitation are solved for the Robertson-Walker space-time, by using a correspondence to known solutions of general relativity.     

Some new Bianchi type-I perfect fluid solutions

We present a simple method to construct some new perfect fluid solutions from known Bianchi type-I solutions.     

Lie group for the Jordan and Brans-Dicke cosmology

A method based on the invariace under a continuous Lie group of transformations is worked out to reduce the problem of finding solutions to the cosmological equations of Jordan and Brans-Dicke theory of gravitation for the Robertson-Walker metrics and the cases of the dust universe and the vacuum universe. The reduction consists in a first-order differential equation and a quadrature for each case. Previously known cosmological solutions are re-obtained. In particular, it becomes apparent during the development of this scheme that the flat-space solutions are indeed the general solution.     

Integral surfaces with space-time coordinates,in the gravitational field of a rotating system

A new integration theory is formulated for dynamical systems with two degrees of freedom, in the gravitational field of a rotating system. Four integrals of motion may be determined from complete solutions of a system of three first-order, partial differential equations in three independent variables. The solutions of this system define two integral surfaces with space-time coordinates. These surfaces represent two independent solutions of a second-order kinematic system to which the original fourth-order system has been reduced. An integral curve may be represented as the locus of intersection points of the integral surfaces. The new theory is the theoretical basis for a method of analytic continuation of periodic orbits of the circular restricted problem.     

A new class of bulk viscous cosmological models in a scale covariant theory of gravitation

Field equations of cosmological models with bulk viscosity are constructed in the scale covariant theory of gravitation. A new class of solutions for the model is found by applying a variable deceleration parameter. Some physical implications of these solutions are briefly discussed.     

Bifurcations of electron acoustic traveling waves in an unmagnetized quantum plasma with cold and hot electrons

Bifurcations of nonlinear electron acoustic solitary waves and periodic waves in an unmagnetized quantum plasma with cold and hot electrons and ions has been investigated. The one dimensional quantum hydrodynamic model is used to study electron acoustic waves (EAWs) in quantum plasma. Applying the well known reductive perturbation technique (RPT), we have derived a Korteweg-de Vries (KdV) equation for EAWs in an unmagnetized quantum plasma. By using the bifurcation theory and methods of planar dynamical systems to this KdV equation, we have presented the existence of two types of traveling wave solutions which are solitary wave solutions and periodic traveling wave solutions. Under different parametric conditions, some exact explicit solutions of the above waves are obtained.     

A class of Szekeres space-times with cosmological constant

We present a generalization of a class of Szekeres space-times. The new solutions satisfy Einstein's equations with a cosmological constant and have the same geometrical properties as the corresponding class found by Szekeres. Particular cases leading to known solutions are considered.     

A new class of bulk viscous FRW cosmological models in a scale covariant theory of gravitation

Friedmann Robertson Walker cosmological models with bulk viscosity are constructed in the scale covariant theory of gravitation. A new class of solutions for the field equations of the model is found by applying variable deceleration parameter. Some physical models of these solutions are briefly discussed in this paper.     

The problem of small divisors in planetary motion

Small divisors caused by certain linear combinations of frequencies appear in all analytical planetary theories. With the exception of the deep resonance between Neptune and Pluto, they can be removed at the expense of introducing secular and mixed secular terms, limiting the domain in which the solution is valid. Because of them classical solutions are known not to converge uniformly; Poincaré referred to them as asymptotic. The KAM theory shows that if one is far enough from exact commensurability and has small enough planetary masses, expansions exist which will converge to quasi-periodic orbits. Solutions showing very small divisors are excluded from this region of convergence. The question of whether they are intrinsic to the problem or are just manifestations of the method of solution is not settled. Problems with a single commensurabily that can be isolated from the rest of the Hamiltonian may have solutions with no small divisors. The problem of two or more commensurabilities remains unsolved.