Higher Dimensional Plane Symmetric Cosmological Models with Two-Fluid Source in General Relativity

We consider anisotropic, homogeneous two-fluid plane symmetric cosmological models in higher dimensions. Here one fluid represents the matter content of the universe and another fluid is chosen to model the CMB (cosmic microwave background) radiation. The radiation and matter content of the universe are in interactive phase. Also we have discussed the behaviour of fluid parameters and kinematical parameters.     

Two Fluids Tilted Cosmological Models in General Relativity

Tilted homogeneous plane symmetric two fluids cosmological models with matter and radiating source are investigated. In the model one of the fluids represents the matter content of the universe and another fluid is the CMB radiation. The tiltedness is also considered .With the help of variation for Hubble’s parameter proposed by Bermann a cosmological model with negative constant deceleration parameter is obtained. We have also investigated the behaviours of some physical parameters.     

Kasner Cosmological Models with Two-Fluid Source in General Relativity

In this paper we present Bianchi type-I metric of the Kasner form describing two-fluid source of the universe in general relativity. In Kasner cosmological models one fluid is a radiation field modeling the cosmic microwave background, while the other is a matter field, modeling material content of the universe. The radiation and matter content of the universe are in interactive phase. We have also presented anisotropic, homogeneous nature of Kasner cosmological models with two-fluid. The behavior of fluid parameters and kinematical parameters of the models are also discussed.     

Bianchi Type-II Bulk Viscous String Cosmological Models in General Relativity

Some Bianchi type II bulk viscous string cosmological models with electromagnetic field are investigated. To get a determinate solution, we assume the shear (σ) is proportional to the expansion (θ), which leads to a supplementary condition B=lA ⁿ , between metric potentials, is used where A and B are function of time alone. A particular solution for n=0 is also discussed. The physical and geometrical implications of the models are discussed.     

Magnetized Bianchi Type III Massive String Cosmological Models in General Relativity

The present study deals with Bianchi type III string cosmological models with magnetic field. The magnetic field is assumed to be along z direction. Therefore F ₁₂ is only the non-vanishing component of electromagnetic field tensor F _ij . The expansion (θ) in the model is assumed to be proportional to the shear (σ). To get determinate solution in term of cosmic time, we have solved the fields equations in two cases (i) Reddy and (ii) Nambu string. The physical and geometrical behaviour of these models is discussed.     

Five Dimensional Axially Symmetric String Cosmological Models with Bulk Viscous Fluid

Bulk viscous fluid distribution with massive strings in LRS Bianchi type-1 space time is studied. The exact solutions of the field equations are obtained by using the equation of state ρ=−λ and ρ=λ. We observed that the bulk viscous fluid does not survive for ρ=−λ whereas it survives for ρ=λ. Some physical and geometrical properties of the models are discussed.     

Plane Symmetric Inhomogeneous Cosmological Models with a Perfect Fluid in General Relativity

In this paper we investigate a class of solutions of Einstein equations for the plane- symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions. PACS No.: 04.20.-q.     

Symmetry Group Analysis for Perfect Fluid Inhomogeneous Cosmological Models in General Relativity

In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between expansion scalar and shear scalar. For this, Lie group analysis is used to identify the generator (isovector fields) that leave the given system of PDEs (Einstein’s field equations) invariant for the models under consideration. A new class of exact solutions of Einstein’s field equation have been obtained for inhomogeneous space-time. The physical behaviors and geometric aspects of the derived models have been discussed in detail.     

Bianchi Type V Cosmological Models with Constant Deceleration Parameter in General Relativity

We investigate Bianchi type V cosmological models with bulk viscous fluid source. Exact solutions of the Einstein field equations are presented via a suitable power law assumption for the Hubble parameter. We show that the corresponding solutions retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Some observational parameters for the models have also been discussed.     

Five Dimensional Bulk Viscous String Cosmological Models in Saez and Ballester Theory of Gravitation

LRS Bianchi type-I bulk viscous string cosmological models are obtained in scalar tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986). It is shown that cosmic string does not survive for ρ+λ=0 whereas it survives for the equations of state ρ=(1+ω)λ (Takabayasi string) and ρ=λ (Geometric string). Some physical and geometrical properties of the exhibited model are discussed.     

Properties of Gravitational Waves in Cosmological General Relativity

The 5D Cosmological General Relativity theory developed by Carmeli reproduces all of the results that have been successfully tested for Einstein's 4D theory. However the Carmeli theory because of its fifth dimension, the velocity of the expanding universe, predicts something different for the propagation of gravity waves on cosmological distance scales. This analysis indicates that gravitational radiation may not propagate as an unattenuated wave where effects of the Hubble expansion are felt. In such cases the energy does not travel over very large length scales but is evanescent and dissipated into the surrounding space as heat.     

Kantowski-Sachs Cosmological Model in General Theory of Relativity

The field equations for perfect fluid coupled with massless scalar field are solved with two conditions p=ρ and R=AS ⁿ for Kantowski-Sachs space time in general theory of relativity. Various physical and geometrical properties of the model have also been discussed.     

Spherically Symmetrical Models in General Relativity

The field equations of general relativity areapplied to pressure-free spherically symmetrical systemsof particles. The equations of motion are determinedwithout the use of approximations and are compared with the Newtonian equations. The total energyis found to be an important parameter, determining thegeometry of 3-space and the ratio of effectivegravitating to invariant mass. The Doppler shift isdiscussed and is found to contain both the velocity shiftand the Einstein shift combined in a rather complexexpression.     

A Higher Dimensional Inflationary Universe in General Relativity

A five dimensional Kaluza-Klein inflationary universe is investigated in the presence of massless scalar field with a flat potential. To get an inflationary universe a flat region in which potential V is constant is considered. Some physical and kinematical properties of the universe are also discussed.     

Cosmological General Relativity with Scale Factor and Dark Energy

In this paper the four-dimensional (4-D) space-velocity Cosmological General Relativity of Carmeli is developed by a general solution of the Einstein field equations. The Tolman metric is applied in the form 1 $$ ds^2 = g_{\mu \nu} dx^{\mu} dx^{\nu} = \tau^2 dv^2 -e^{\mu} dr^2 - R^2 \left(d{\theta}^2 + \mbox{sin}^2{\theta} d{\phi}^2 \right), $$ where g _μν is the metric tensor. We use comoving coordinates x ^α = (x ⁰, x ¹, x ², x ³) = (τv, r, θ, ?), where τ is the Hubble-Carmeli time constant, v is the universe expansion velocity and r, θ and ? are the spatial coordinates. We assume that μ and R are each functions of the coordinates τv and r. The vacuum mass density ρ _Λ is defined in terms of a cosmological constant Λ, 2 $$ \rho_{\Lambda} \equiv -\frac{ \Lambda } { \kappa \tau^2 }, $$ where the Carmeli gravitational coupling constant κ = 8πG/c ² τ ², where c is the speed of light in vacuum. This allows the definitions of the effective mass density 3 $$ \rho_{eff} \equiv \rho + \rho_{\Lambda} $$ and effective pressure 4 $$ p_{eff} \equiv p - c \tau \rho_{\Lambda}, $$ where ρ is the mass density and p is the pressure. Then the energy-momentum tensor 5 $$ T_{\mu \nu} = \tau^2 \left[ \left(\rho_{eff} + \frac{p_{eff}} {c \tau} \right) u_{\mu} u_{\nu} - \frac{p_{eff}} {c \tau} g_{\mu \nu} \right], $$ where u _μ = (1,0,0,0) is the 4-velocity. The Einstein field equations are taken in the form 6 $$ R_{\mu \nu} = \kappa \left(T_{\mu \nu} - \frac{1} {2} g_{\mu \nu} T \right), $$ where R _μν is the Ricci tensor, κ = 8πG/c ² τ ² is Carmeli’s gravitation constant, where G is Newton’s constant and the trace T = g ^αβ T _αβ . By solving the field equations (6) a space-velocity cosmology is obtained analogous to the Friedmann-Lemaître-Robertson-Walker space-time cosmology. We choose an equation of state such that 7 $$ p = w_e c \tau \rho, $$ with an evolving state parameter 8 $$ w_e \left(R_v \right) = w_0 + \left(1 - R_v \right) w_a, $$ where R _v = R _v (v) is the scale factor and w ₀ and w _a are constants. Carmeli’s 4-D space-velocity cosmology is derived as a special case.     

Plane Symmetric String Cosmological Model in Modified Theory of General Relativity

It is shown that homogeneous plane symmetric string cosmological model for Takabayasi string i.e. ρ=(1+ω)λ does not exist in Barber’s second self creation theory. Further it is found that the string cosmological model in this theory exist only when ω=0. Therefore model for ρ=λ (geometric string) is constructed. Some physical and geometrical properties of the model are discussed.     

Extending the Redshift-Distance Relation in Cosmological General Relativity to Higher Redshifts

The redshift-distance modulus relation, the Hubble Diagram, derived from Cosmological General Relativity has been extended to arbitrarily large redshifts. Numerical methods were employed and a density function was found that results in a valid solution of the field equations at all redshifts. The extension has been compared to 302 type Ia supernova data as well as to 69 Gamma-ray burst data. The latter however do not truly represent a ‘standard candle’ as the derived distance moduli are not independent of the cosmology used. Nevertheless the analysis shows a good fit can be achieved without the need to assume the existence of dark matter. The Carmelian theory is also shown to describe a universe that is always spatially flat. This results from the underlying assumption of the energy density of a cosmological constant Ω_Λ=1, the result of vacuum energy. The curvature of the universe is described by a spacevelocity metric where the energy content of the curvature at any epoch is Ω _K =Ω_Λ−Ω=1−Ω, where Ω is the matter density of the universe. Hence the total density is always Ω _K +Ω=1.     

Bianchi Type-III Magnetized Wet Dark Fluid Cosmological Model in General Relativity

Bianchi type-III cosmological model of universe filled with dark energy from a wet dark fluid (WDF) in presence and absence of magnetic field is investigated in general theory of relativity. We assume that F ₁₂ is the only non-vanishing component of F _ij . We obtain exact solutions to the field equations using the condition that expansion is proportional to the shear scalar i.e. (B=C ⁿ ). The physical behavior of the model is discussed with and without magnetic field. We conclude that universe model do not approach isotropy through the evolution of the universe.     

Bianchi Type I Magnetized Barotropic Perfect Fluid Cosmological Model in General Relativity

Bianchi Type I barotropic perfect fluid cosmological model in presence of magnetic field, is investigated. To get the deterministic model, we have also assumed that σ ₁¹ α θ where σ ₁¹ is the eigen-value of shear tensor σ _i ^j and θ the expansion in the model. The behavior of the model in presence and absence of magnetic field and singularities in the model are also discussed.