On the scalar-tensor theory of Lau and Prokhovnik

Recently Lau & Prokhovnik (1986) have formulated a new scalar-tensor theory of gravitation which reconciles Dirac’s large numbers hypothesis with Einstein’s theory of general relativity. The present work points out an error in the time-dependent cosmological term and the scalar potential given by Lau and Prokhovnik. The correct forms for these quantities are derived. Further, a vacuum Robertson-Walker solution to the generalized field equations is obtained, under an anasatz that we propose, which illustrates that the theory is, in some sense, incomplete.     

(An)Isotropic models in scalar and scalar-tensor cosmologies

We study how the constants G and Λ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (“quintessence”) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi V, VII₀ and IX, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive at the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function.     

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).     

Inhomogeneous Mesonic Perfect Fluid Models in Modified Theory of General Relativity

In this paper, we have investigated plane symmetric inhomogeneous cosmological models in the presence of massless scalar field in modified theory of general relativity when source of the gravitational field is a perfect fluid. The physical and geometrical aspects of the models together with singularity involved in the models are also discussed. PACS Nos.: 04.50. + h•4.20.Cv• 4.20.Dw     

Cosmological scalar fields that mimic the ΛCDM cosmological model

We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard ΛCDM cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble parameter (i.e. photometric distance and angular diameter distance as functions on z). Asymptotic behavior of the field solutions is studied in the case of spatially flat Universe with pressureless matter and separable scalar field Lagrangians; the cases of power-law kinetic term and power-law potential are considered. Exact analytic solutions are found in some special cases. A number of models have the field solutions with infinite behavior in the past or even singular behavior at finite redshifts. We point out that introduction of the cosmological scalar field involves some degeneracy leading to lower precision in determination of Ω _m . To remove this degeneracy additional information is needed besides the data on large-scale geometry. The article is published in the original.     

Quintessential inflation models with a nonminimally coupled scalar field

The evolution of a homogeneous, isotropic cosmological model driven by a nonminimally coupled scalar field is studied. The potential for the quintessential inflation model proposed by Peebles and Vilenkin is selected as a scalar potential. Possible scenarios for the cosmological dynamics are described in the conformal Einstein and Jordan representations. It is shown that, unlike in models with a minimal scalar field, here a class of solutions exists for which the scalar field is fixed at finite values during cosmological expansion. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 487–498 (August 2006).     

Global Monopole and C-Field

It is well known that a C-field, generated by a certain source equation leads to interesting changes in the cosmological solutions of Einstein's equations. It is argued that different types of topological objects may have been created by the vacuum phase transitions in the early universe. In the cosmological arena, the defects have been put forward as a possible mechanism for structure formation. A global monopole is a heavy object formed in the phase transition of a system composed of a self coupling scalar field triplet φ^a whose original global 0(3) symmetry is spontaneously broken to U(1). In this article, we find a special solution for the space-time of a global monopole in presence of C-field. It is shown that the nature of the solution remains the same as in general relativity case i.e. monopole exerts no gravitational force on the matter surrounding it but space around it has a deficit solid angle. Pacs Nos: 98.80cq, 04.20jb, 04.50     

Inhomogeneous cosmological models in the presence of massless scalar fields

Non-static inhomogeneous cosmological models are obtained in general relativity for the case of a plane symmetric massless scalar field with cosmological constant A,when the source of the gravitational field is a viscous fluid.Some physical and geometrical behaviors of the solutions are also discussed.     

Anisotropic cosmological model with variable G and Λ

Anisotropic Bianchi-III cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein’s general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Λ are discussed. Without assuming any specific forms for Λ and the metric potentials, we have tried to extract the time variation of G and Λ from the anisotropic model. The extracted G and Λ are in conformity with the present day observations. Basing upon the observational limits, the behavior and range of the effective equation of state parameter are discussed.     

Incompatibility of five dimensional LRS Bianchi type-V string and mesonic string cosmological models in general relativity

In this paper, we constructed some cosmological models in five dimensional LRS Bianchi type-V space time based on general theory of relativity. Further, it is shown that source density of the meson field does not survive either in massive scalar field or in mass less scalar field. Some physical and geometrical properties of the models are discussed.     

Dilaton stabilization in string cosmology. I

A new mechanism is proposed for stabilization of the scalar dilaton field within the framework of lowenergy string gravitation with loop corrections to the dilaton coupling functions. It is based on the assumption that the loop corrections generate a kinetic dilaton function, which is singular for some finite value of the dilaton field. For a nongravitational source of the barotropic type, the system of equations describing the evolution of homogeneous and isotropic cosmological models is represented in the form of a thirdorder, autonomous, dynamical system. The behavior of the general solution in the vicinity of singularities of the dilaton coupling function is investigated by methods of the qualitative theory of dynamical systems. It is shown that there is a class of solutions, different from solutions of the general theory of relativity, with a constant dilaton. The conditions under which these solutions are an attractor for a general solution with a variable dilaton are determined. Translated from Astrofizika, Vol. 43, No. 1, pp. 123-136, January–March, 2000.     

Exact Kantowski–Sachs cosmological models in general theory of relativity

We have studied cosmological model generated by perfect fluid coupled with mass less scalar field for Kantowski–Sachs space–time in general theory of relativity. Two different physically viable models of the universe are obtained by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. Some physical consequences of the models have been discussed in case of Zel’dovich fluid.     

Brans-Dicke Quantum Cosmology

By solving a Wheeler-De Witt ‘extended’ equation in the Brans-Dicke theory, we have found that the probability distribution predicts: i) An initial value for the Brans-Dicke scalar field φ ∼ ρ^1/2_VAC in the beginning of the inflation, where ρ_VAC is the vacuum density energy (this gives a planck mass ∼ ρ^1/4_VAC) ii) Large values for the Brans-Dicke parameter w. On the other hand it is shown that by taking into account the dynamical behaviour of φ and the matter scalar field σ we can formulate a ‘creation boundary condition’ where in the ‘beginning’ of the Universe (R =0, ‘nothing’ for some authors) we have a dynamical σ already ‘created’. This could be the energetic mechanism which makes Universe tunnels the potential barrier to evolve classically after. Besides we have found the possibility of a cosmological uncertainty principle. This revised version was published online in July 2006 with corrections to the Cover Date.     

Conformal analogs of the Jordan-Brans-Dicke theory. I.

Recent cosmological observations of large-scale structures (red shift of type Ia supernovae) confirm that the universe is currently expanding at an accelerating rate and its dominant component is dark energy. This has stimulated the development of the theory of gravity and led to many alternative variants, including tensor-scalar ones. This paper deals with the role of conformal transformations in the Jordan-Brans-Dicke theory. Variants of intrinsic, conformally coupled, and Einstein representations are examined. In the Einstein representation an exact analytic solution for the standard cosmological model is obtained. It is expressed in terms of the relative energy contributions of ordinary matter Ω _m , the scalar field Ω _CK , and a term Ω_Λ related to the cosmological constant Λ . Information on the evolution of the universe for the case with a minimally coupled scalar field is given in the form of graphs.     

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 Scalar Field Cosmology with Causal Viscous Fluid

An exact cosmological solution for Friedman Robertson Walker (FRW)metric is obtained with a classical scalar field φ along with a potential in the presence of a causal viscous fluid. Assuming the scale factor to be a function of the scalar field we have obtained solutions in both the truncated and the full causal theory. It is shown that an inflationary model can be obtained by imposing certain constraints on some constants. The radiative bulk viscosity during the decoupling era has also been studied as a special case. This revised version was published online in July 2006 with corrections to the Cover Date.     

Role of a scalar field in the radiation dominated epoch of the development of the universe

The recently discovered accelerated expansion of the universe is of current interest in theoretical research on the evolution of the universe. The cause of this behavior is presumably the presence of dark energy, which has been estimated to form up to 70% of the universe and generates a “repulsive force.” In this paper a cosmological model is constructed which takes the dark energy into account in a Jordan-Brans-Dicke tensor-scalar model with a dominant, nonminimally coupled scalar field in the presence of a cosmological scalar. The radiation dominant epoch is discussed. __________ Translated from Astrofizika, Vol. 51, No. 1, pp. 151–159 (February 2008).     

Exact Bianchi Type-I Cosmological Micro Model in Modified Theory of General Relativity

An anisotropic, homogeneous Bianchi type-I cosmological micro model is obtained in Barber's modified theory of general relativity. Some properties of the model are discussed. Further, it is found that this theory leads to Einstein theory as the coupling parameterλ → 0 in micro level (i.e., quantum level) in general. This revised version was published online in July 2006 with corrections to the Cover Date.     

String fluid cosmological models in general relativity

LRS Bianchi type-I string cosmological models are studied in the frame work of general relativity when the source for the energy momentum tensor is a bulk viscous fluid containing one dimensional strings embedded in electromagnetic field. A barotropic equation of state for the pressure and density is assumed to get determinate solutions of the field equations. The bulk viscosity is assumed to be inversely proportional to the scalar expansion. The physical and kinematical properties of the models are discussed. The effect of viscosity and electromagnetic field on the physical and kinematical properties is also investigated.