Some results in the general scalar tensor theory

Raychaudhuri-type equations are written for a cosmological model filled with a perfect fluid and obeying the equations of general scalar-tensor theory proposed by Nordtvedt. It is found that a non-rotating cosmological model may, in general, have a minimum volume. The Hawking-Penrose energy condition suggests that the singularity can be avoided in this theory.     

An inflationary cosmological model in Dunn's scalar-tensor theory of gravitation

The gravitational field equations in Dunn's scalar-tensor theory of gravitation are generalized by including a cosmological constant. The resulting equations are solved for a Robertson-Walker line-element with flat three-space. The solution represents a cosmological model that develops into an inflationary era.     

Bianchi type-V bulk viscous cosmological models with particle creation in Brans-Dicke theory

The Bianchi type-V cosmological model with viscous fluid and creation particle in Brans-Dicke theory has been considered. The present paper deals with Bianchi type-V cosmological model with bulk viscosity and particle creation described by full causal thermodynamics in Brans-Dicke theory. We have discussed two types of solutions of the average scale factor for a Bianchi type-V model by using a variation law of Hubble’s parameter, which yields a constant value of the deceleration parameter. The exact solutions to the corresponding field equations are obtained in quadrature form. The solutions to the Einstein field equations are obtained for power law and exponential form. The cosmological parameters have been discussed in detail.     

Modified equations in the theory of induced gravity. Solution to the cosmological constant problem

This research is an extension of the author’s works, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein’s theory of gravity and string theory. This work is devoted to the formation of self-consistent equations of the theory of induced gravity in the presence of matter in the form of a perfect fluid that interacts with scalar fields. The study is done to solve these equations for the case of the cosmological model. In this model time-evolving gravitational and cosmological “constants” take place which are determined by the square of scalar fields. The values of which can be matched with the observational data. The equations that describe the theory have solutions that can both match with the solutions of the standard theory of gravity as well as it can differ from it. This is due to the fact that the fundamental “constants” of the theory, such as gravitational and cosmological, can evolve over time and also depend of the coordinates. Thus, in a rather general case the theory describes the two systems (stages): Einstein and “evolving”. This process is similar to the phenomenon of phase transition, where the different phases (Einstein gravity system, but with different constants) transit into each other.     

Non-vacuum cosmological solutions of 5D variable mass theory of gravity

A class of non-vacuum expanding cosmological solutions of Wesson's 5D theory of gravity with variable rest mass is derived. The models are spatially homogeneous and isotropic and the source of gravitation is a pressureless fluid (dust) plus a cosmological constant term. The general and unified solution is found for the equations and some properties of different limiting cases are studied. Particularly, it is shown that for null cosmological constant the predicted age of the universe is smaller than the ones of the 4D FRW models.     

Theory of linear cosmological perturbations in flat space-time theory of gravitation

Covariant linear cosmological perturbations are considered in flat space-time theory of gravitation. The background metric is not altered. The perturbed energy-momentum is given. The basic equations for the propagation of the perturbations are presented. The perturbed equations for a homogeneous, isotropic universe are stated.     

Exact Brans-Dicke bianchi type-I vacuum solutions with a cosmological constant

Exact cosmological solutions of the vacuum Brans-Dicke field equations are derived. The solutions are the anisotropic generalizations of the isotropic de Sitter solutions of the general theory of relativity.     

Higher Dimensional String Cosmologies in Scale-Covariant theory of Gravitation

Field equations are obtained with the aid of higher dimensional Bianchi type-I cosmological model in scale covariant theory of gravitation in the context of cosmic strings. We present here isotropic and anisotropic solutions of the field equations and some physical implications of these solutions are briefly discussed.     

Spherically symmetric cosmological perturbation in a universe with background field

In a previous paper the equations of small cosmological perturbations of a theory of gravitation in flat space-time are derived. They are applied to a homogeneous, isotropic, nonsingular cosmological model with radiation, matter and background field. At the beginning of the universe small spherically symmetric inhomogeneities on almost all scales can arise by instability. Later on the density contrast of dust grows exponentially during a short time epoch. The solution during this time period is given analytically.     

Perihel-Bewegung und kosmologische Singularität in TREDERS Gravitationstheorie

In the framework of TREDER 's gravitational theory we elaborate the consequences of a class of field equations for some solar-system effects and their connection to the problem of cosmological singularity. These equations read on special conditions with components of the energy momentum tensor, KRONECKER 's symbol, tetrad components). ω is a real parameter. If we choose the integration constants of the static spherically symmetric vacuum case in such a way that red shift is the same like that of EINSTEIN 's theory and the source of gravitational field is that of a point mass we obtain for the perihelion rotation the expression is EINSTEINS value of the perihelion rotation.) For we obtain But only if ω > 2/5 cosmological models exist which have no cosmological singularity. On the other hand for ω > 2/5 the value is greater than.     

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.     

Linear perturbations in a universe with a cosmological constant

There is now evidence that the cosmological constant Λ has a non-zero positive value. Alternative scenarios to a pure cosmological constant model are provided by quintessence, an effective negative pressure fluid permeating the Universe. Recent results indicate that the energy density ρ and the pressure p of this fluid are constrained by − ρ ≤ p ≲−0.6 ρ . As p =− ρ is equivalent to the pure cosmological constant model, it is appropriate to analyse this particular, but important, case further.
We study the linear theory of perturbations in a Friedmann–Robertson–Walker universe with a cosmological constant. We obtain the equations for the evolution of the perturbations in the fully relativistic case, for which we analyse the single-fluid and two-fluid cases. We obtain solutions to these equations in appropriate limits. We also study the Newtonian approximation. We find that for a positive cosmological constant universe (i) the perturbations will grow more slowly in the relativistic regime for a two-fluid composed of dark matter and radiation, and (ii) in the Newtonian regime the perturbations stop growing.     

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.     

Some general results in modified Brans-Dicke cosmologies

Raychaudhuri-type equations are derived for cosmological models filled with a perfect fluid and obeying the Brans-Dicke equations with a cosmological term depending on the scalar field. In addition, some general results on spatially homogeneous cosmological models are obtained in the theories due to Bergmann and Wagoner and Uehara and Kim.     

The general class of Bianchi cosmological models with viscous fluid and particle creation in Brans-Dicke theory

This paper deals with the general class of Bianchi cosmological models with bulk viscosity and particle creation described by full causal thermodynamics in Brans-Dicke theory. We discuss three types of average scale-factor solutions for the general class of Bianchi cosmological models by using a special law for the deceler- ation parameter which is linear in time with a negative slope. The exact solutions to the corresponding field equations are obtained in quadrature form and solutions to the Einstein field equations are obtained for three different physically viable cosmologies. All the physical parameters are calculated and discussed in each model.     

Turbulence in cosmology

Principles of the theory of turbulence in relativistic cosmology are developed. By averaging Einstein's equations over stochastic fields a self-consistent system of equations is obtained which describes statistically: (1) the influence of the turbulence on the ‘basic state of the Universe (the background) on which the turbulence develops; (2) the behaviour of the turbulence on the background ‘distorted’ by it. By means of a qualitative study of exact equations in the region of a strong turbulence at an early stage of cosmological expansion conditions of the absence of singularity are found and the possibility of stationary solutions in the homogeneous, isotropic, on the average, Universe (the cosmological constantA=0) is shown. The rate of cosmological expansion increases if the energy density of the turbulence is positive, and decreases if it is negative. The latter alternative takes place if the absolute value of the energy density of excitations, which will change into potential motions in the future, exceeds the energy density of the remaining part of the turbulence.     

Exact self-creation cosmological solutions

Under the assumption of a power law between the expansion factor of the Universe and the scalar field of the second self-creation theory proposed by G. A. Barber, the cosmological equations are reduces to quadratures. Several exact solutions are obtained, among them linearly expanding and inflationary universes with a barotropic equation of state.     

Varying Fundamental Constants from a String-inspired Brane World Model

We report results on the construction of cosmological braneworld models in the context of the Einstein-Gauss-Bonnet gravity, which include the leading correction to the Einstein-Hilbert action suggested by superstring theory. We obtain and study the equations governing the dynamics of the standard cosmological models. We find that they can be written in the same form as in the case of the Randall-Sundrum model but with time-varying four-dimensional gravitational and cosmological constants. Finally, we discuss the cosmological evolution predicted by these models and their compatibility with observational data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Einstein-Rosen Universe in the Scale-Covariant Theory of Gravitation

Field equations in the presence of a perfect fluid distributionc for Einstein-Rosen cylindrically symmetric metric are obtained in the scale-covariant theory of gravitation proposed by Canuto et al. (1977a). A static vacuum model and a non-static cosmological model corresponding to perfect fluid are presented. Physical and Kinematical properties of the models are also discussed.     

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.