Homogeneous Isotropic Cosmological Models Research Articles

Phantom scalar fields in five-dimensional Kaluza-Klein theory

The existence of a so-called "phantom" scalar field in some Riemannian spaceV4, i.e., a field in which the effective energy momentum tensorT(sf) vanishes in the five-dimensional Kaluza-Klein theory, is investigated by means of the integrability conditions for relations of the form Φ;μ;ν=kΦ,μΦ,ν+bgμν found in [6]. Phantom fields are found in homogeneous isotropic cosmological models.

Shear-free, irrotational, geodesic, anisotropic fluid cosmologies

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a co-moving observer, satisfy an equation of state of the form , with , then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.

Relativistic hydrodynamics and gravitational instability revisited

After some 90 years of effort, the phenomenon of gravitational instability elucidated by Jeans continues to attract much attention and to reveal an unexpected richness of structure. A unified and simplified treatment of recent development in this area is presented, and extended to give new, completely general, exact second-order acoustic propagation equations, governing the evolution of the comoving fractional spatial gradient of the density. Newtonian theory and general relativity are considered, and the unity of the two points of view is emphasized. The Einstein static universe and expanding homogeneous isotropic cosmological models are re-examined

Cosmological solution in wesson's 5D theory of gravity

Cosmological solutions that obey the perfect fluid equation of state in Wesson's gravitational theory are presented assuming that the fifth dimension subspace is also homogeneous and isotropic like the usual homogeneous isotropic cosmological model. It is shown that the scale factor scales as\(\sqrt t \) for the vanishing fifth component of the energy momentum tensor. The role of the fifth component as a cosmological constant is remarked, and an inflationary model is thus obtained.

A quantized flat homogeneous isotropic cosmological model

The limiting case of the solutions considered in our previous paper and the paper of Burlankov et al., which corresponds to the infinite radius of space curvature, is a flat-space model. This work completes a series of papers on the quantization of homogeneous isotropic cosmological models filled with elastic gas with the phenomenological compressibility law suggested by Burlankov, Dutyshev and Kochnev.

A quantized open homogeneous isotropic cosmological model

In the present investigation the problem of the quantization of an open homogeneous isotropic model of the universe with elastic gas is exactly solved. The equation of state for a low-density gas corresponds to the case of dust-like matter; for a high-density gas it corresponds to the ultrarelativistic case.

Relativistie Cosmology With Quantum Corrections

Homogeneous isotropic, anisotropic, and inhomogeneous cosmological models are studied using Einstein's general relativity with quntum corrections in field theoretical approximation. In particular we discuss coherent scalar fields and curvature squared terms in the gravitational Lagrangian. The conformal equivalence of the field equations of fourth order to general relativity with a scalar field as source is an example of the geometrization of a matter field. The aemiclassical quantum eorrections of the scalar fields can avoid the initial cosmological singularity and they lead to an inflationary evolution stage as transient attrator. The review provides new points of view on questions like the probability of the inflationary stage and the question of mechanisms for multiple inflation.

Perturbations of Friedmann-Robertson-Walker cosmological models

The mathematical principles underlying the theory of gauge-invariant perturbations of homogeneous isotropic cosmological models are discussed and a collection of useful formulae is given.

Quantum cosmology with fermionic matter

The quantum evolution of homogeneous isotropic cosmological models with ferm ionic matter described by spinor fields is investigated within the framework of the formalism of superspace quantization. The fact that quadratic combinations of fermionic operators (current density, spin density, Lagrangian, etc.) are bosonic operators and admit an explicit Schrodinger representation is used in an essential way. It is shown that the DeWitt equation for the cosmological models with fermionic matter under consideration has the form of the Schrodinger equation, so that a correct definition is possible for the probability density of the existence of the models under consideration, in which the singularity is removed.

Homogeneous Isotropic Cosmology on the Basis of a New 5‐Dimensional Projective Unified Field Theory

AbstractThe previously elaborated Projective Unified Field Theory (PUFT) of the author is applied to a homogeneous isotropic cosmological model generalising the Friedman model. The following special cases are treated: dust model and electromagnetic radiation model.

Scalar fields in cosmology with an exponential potential

A homogeneous isotropic cosmological model driven by a scalar field with an exponential potential is studied. It is shown that there is a solution with power-law inflation, and this solution is an attractor. Some examples of theories which lead to an exponential potential are discussed.

Localization of the Einstein group and a nonsingular cosmological model of space-time with torsion

We consider an Einstein-invariant gauge theory of gravitation (EGT), obtained by localizing the group of motions of a homogeneous static Einstein Universe. Taking into account the cosmological term, we find exact solutions of EGT are as nonsingular homogeneous Isotropic cosmological models with both the metric and the torsion regular. It is shown that EGT satisfies the principle of correspondence with Newton's theory of gravity and with the tetrad theory of gravity in the space of absolute parallelism.

Inflationary stages in cosmological models with a scalar field

Homogeneous isotropic cosmological models with a massive scalar field are studied. It is shown that inflationary stages of evolution are characteristic of most solutions in these models.

Numerical calculations of minisuperspace cosmological models

The wave function of the universe is calculated numerically by solving the zero energy Schrödinger equation for homogeneous isotropic cosmological models with a massive scalar field or with curvature squared corrections to the action. The boundary condition used to integrate the equation is that the wave function should be given by a path integral over compact metrics.

Homogeneous isotropic cosmological model in a new scalar-tensor theory

A Friedmann-Robertson-Walker (FRW) model is studied in the new scalar-tensor theory of gravitation proposed by Schmidt et al. There is an assumption of a particular functional relationship between the cosmological expansion factor of the FRW model and the scalar field. Exact solutions are given, and it is observed that at least in one case $k=\ensuremath{-}1$ it is possible to obtain a model with oscillation between finite limits.

The unified field theory, combining Kaluza's five-dimensional and Weyl's conformal theories

A version of the five-dimensional unified theory of gravitation, electromagnetism, and scalar field is developed. It is shown that in this theory the main features of Kaluza's five-dimensional theory and the Weyl one, based on non-Riemannian geometry and on conformal mapping, are combined. Some reasons are pointed out for choosing the physical 4-metric to be conformal (with the factorϕ2=−G55) to the 4-metric obtained by 1+4 splitting of the initial five-dimensional manifold. It is shown that the electrical charge and current appear in the geometrical theory if the condition of cylindrical symmetry in the fifth coordinate is substituted by the condition of quasicylindrical symmetry (i.e., the physical 4-metric and the vector potential of electromagnetic field remain independent of the fifth coordinate, while the scalar field depends on it). Two kinds of the most important exact solutions of the 15 field equations are considered. They are (1) static spherically symmetrical solutions and (2) homogeneous isotropic cosmological models.

Quantization of a homogeneous isotropic cosmological model in five-dimensional field theory

Quantization of a homogeneous isotropic cosmological model in five-dimensional field theory

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=ɛ/3.

A cosmological model in the bimetric gravitation theory

In the framework of the bimetric theory of gravitation a homogeneous isotropic cosmological model is set up having negative spatial curvature (k=-1) and containing matter having negligible pressure. The solutions of the field equations are obtained as expansions in powers of a small parameter, the present value of which can be determined, in principle, from observational data. It appears that its order of magnitude is such that the PPN parameter ..cap alpha../sub 2/ considered by Lee et al. is small enough to make the bimetric theory viable. The rate of change with time of the gravitational constant is found to be considerably smaller than the present estimated upper limit.

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.