Bianchi Type I string dust cosmological model with magnetic field in general relativity

Bianchi Type I string dust cosmological models in presence and absence of magnetic field following the techniques used by Letelier and Stachel, are investigated. To get the deterministic solution, we have assumed that σ ₁¹ is proportional to the expansion (θ) where σ ₁¹ is the eigen value of shear tensor (σ _i ^j ) and which leads to A=N(BC)⁻ⁿ , n>0 where A,B,C are metric potentials and , N and ℓ are constants. The behaviour of the models in presence and absence of magnetic field are discussed. The other physical and geometrical aspects of the model are also discussed.     

Bianchi Type I Magnetized String Cosmological Model in General Relativity

Bianchi Type I magnetized string cosmological model following the techniques used by Letelier and Stachel, is investigated. To get a determinate model, we assume a condition ∊ = λ (geometric string) where ∊ is the rest energy density, λ the string tension density and expansion (θ) is proportional to eigen value σ₁ ¹ of shear tensor (σ _j ⁱ ), which leads to A = ℓ (BC) ⁿ where A, B, C are metric potentials and ℓ and n are constants. The behaviour of the model in presence and absence of magnetic field is discussed. The physical and geometrical aspects of the model are also discussed.     

LRS Bianchi-I anisotropic cosmological model with dominance of dark energy

The present study deals with spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with dominance of dark energy. To get the deterministic model of Universe, we assume that the shear scalar (σ) in the model is proportional to expansion scalar (θ). This condition leads to A=B ⁿ , where A, B are metric potential and n is positive constant. It has been found that the anisotropic distribution of dark energy leads to the present accelerated expansion of Universe. The physical behavior of the Universe has been discussed in detail.     

Kantowski-Sachs String Cosmological Model with Bulk Viscosity In General Relativity

String cosmological models with bulk viscosity are investigated in Kantowski-Sachs space-time. To obtain a determinate solution, it is assumed that the coefficient of bulk viscosity is a power function of the scalar of expansion ζ = kθ^m and the scalar of expansion is proportional to the shear scalar θ ∝ σ, which leads to a relation between metric potentials R = AS ⁿ . The physical and geometrical aspects of the model are also discussed. It is shown that the bulk viscosity has significant influence on the evolution of the universe. There is a ‘big bang’ start in the model when m ≤ 1 but there is no ‘big bang’ start when m > 1.     

An LRS Bianchi Type I Bulk Viscous Fluid String Cosmological Model in General Relativity

An LRS Bianchi type I string dust cosmological model with and without bulk viscosity following a method used by Letelier and Stachel, is investigated. To get a determine solution, it is assumed that σ∝θ whereσ is shear and θ is scalar of expansion and which leads to A =αBⁿ were n is a constant. The physical and geometrical aspects of the model are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bulk viscous LRS Bianchi-I Universe with variable G and decaying Λ

The present study deals with spatially homogeneous and totally anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with variable G and Λ in presence of imperfect fluid. To get the deterministic model of Universe, we assume that the expansion (θ) in the model is proportional to shear (σ). This condition leads to A=ℓB ⁿ , where A, B are metric potential. The cosmological constant Λ is found to be decreasing function of time and it approaches a small positive value at late time which is supported by recent Supernovae Ia (SN Ia) observations. Also it is evident that the distance modulus curve of derived model matches with observations perfectly.     

Bianchi type-III non-static magnetized cosmological model for perfect fluid distribution in general relativity

We have investigated Bianchi type III non-static magnetized cosmological model for perfect fluid distribution in general relativity. We assume that F ₁₂ is the only non-vanishing component of F _ij . Maxwell’s equation

Some Bianchi type cosmological models in f(R) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. In this context, we study the exact vacuum solutions of Bianchi type I, III and Kantowski-Sachs spacetimes in the metric version of f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives A=B ⁿ , where A and B are the metric coefficients. The physical behavior of the solutions has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated in each case.     

Some magnetized bulk viscous string cosmological models in?General Relativity

Some Bianchi type-I viscous fluid string cosmological models with magnetic field are investigated. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density ξ(t)=ξ ₀ ρ ^m , where ξ ₀ and m are constants. To get a determinate model, we assume conditions ρ=(1+ω)λ, where ρ is rest energy density, ω a positive constant and λ the string tension density and expansion θ is proportional to eigen value σ ₁¹ of the shear tensor σ _j ⁱ . The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field is discussed.      

Expanding and shearing magneto-viscous fluid cosmological model in general relativity

The object of this paper is to investigate the behavior of a magnetic field in a viscous fluid cosmological model. It has been assumed that the expansion () is proportional to the eigenvalue ₁ of the shear tensor _i ^j and the coefficient of shearing viscosity is proportional to the scalar of expansion. The paper also discusses the behavior of the model when the magnetic field tends to zero and comments on some other physical properties.     

LRS Bianchi type-II massive string cosmological model in General Relativity

The present study deals with locally rotationally symmetric (LRS) Bianchi type II cosmological model representing massive string. The energy-momentum tensor for such string as formulated by Letelier (Phys. Rev. D 28:2414, 1983) is used to construct massive string cosmological model for which we assume that the expansion (θ) in the model is proportional to the shear (σ). This condition leads to A=B ^m , where A and B are the metric coefficients and m is proportionality constant. For suitable choice of constant m, it is observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Our model is in accelerating phase which is consistent to the recent observations of type Is supernovae. Some physical and geometric behavior of the model is also discussed.     

Generalized Expanding and Shearing Anisotropic Bianchi Type I Magnetofluid Cosmological Model in General Relativity

The behaviour of magnetic field in anisotropic Bianchi type I cosmological model for perfect fluid distribution in General Relativity, is investigated. The distribution consists of an electrically neutral perfect fluid with an infinite electrical conductivity. It is assumed that the component ¹ ₁ of shear tensor ^j _i is proportional to the expansion () which leads to A = (BC)ⁿ. The other physical and geometrical aspects of the model are also discussed, Bali (1986) obtained the cosmological model for n = 1 in presence of magnetic field. We have investigated the model for general values of n and discussed the particular case and general behaviour of the model.     

Tilted Bianchi Type I Cosmological Models for Barotropic Perfect Fluid in General Relativity

In this paper, we have investigated that tilted Bianchi Type I cosmological models for stiff perfect fluid under a supplementary condition A = B ⁿ between metric potentials, is not possible. The tilted solution is also not possible when we assume A = t ^ℓ, B = t ^m , C = t ⁿ ; ℓ, m and n are constants for ε = p. Thus to preserve tilted nature of model, we assume p = γε, 0 ≤ γ ≤ 1 (barotropic equation of state) for the case A = t ^ℓ B = t ^m and C = t ⁿ . The physical and geometrical aspects of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cylindrically symmetric inhomogeneous universe with electromagnetic field in string cosmology

Cylindrically symmetric inhomogeneous string cosmological model in presence of electromagnetic field is investigated. We have assumed that F ₂₃ is the only non-vanishing component of F _ij . To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ ¹ ₁ of the shear tensor σ ⁱ _j . The physical and geometric aspects of the model are also discussed.      

Bianchi type-VI0 perfect fluid cosmological models with magnetic field

In this paper we discuss Bianchi type-VI₀ cosmological models with perfect fluid distribution and magnetic field directed along the axial direction. Einstein's equations have been solved for the condition that the expansion scalar bears a constant ratio to the anisotropy in the direction of a space-like unit vector ⁱ.     

The equivalence between different Dark (matter) energy scenarios

We have shown that the phenomenological models with a cosmological constant of the type Λ=β( ) and Λ=3αH ², where R is the scale factor of the universe and H is the Hubble constant, are equivalent to a quintessence model with a scalar (φ) potential of the formV∝φ^-n, n= constant. The equation of state of the cosmic fluid is described by these parameters (α, β, n) only. The equation of state of the cosmic fluid (dark energy) can be determined by any of these parameters. The actual amount of dark energy will define the equation of state of the cosmic fluid.All of the three forms can give rise to cosmic acceleration depending the amount of dark energy in the universe.     

Bianchi Type I String Cosmological Models with Bulk Viscosity and Magnetic Field

Some locally rotationally symmetric (LRS) Bianchi type I cosmological models for a cloud string with bulk viscosity and magnetic field are presented. Where an equation of state ρ = kλ and a relation between metric potential R = AS ⁿ are considered. The solution describes a shearing and nonrotating model with a big bang start. In the absence of magnetic field it reduces to a string model with bulk viscosity, where the relation between the coefficient of bulk viscosity and energy density is ζ ∝ ρ^1/2. After choosing k = , it further reduces to a string model without viscosity and magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.     

Exact cosmological solutions in the scalar-tensor theory with cosmological constant

Under the assumption of a power-law between the expansion factor of the Universe, and the scalar field (a ⁿ=c=const.) tensor theory with cosmological constant are reduced to quadrature. Several exact solutions are obtained, among them inflationary universes that have barotropic equation of state.     

Periodic solutions for resonance 4/3: Application to the construction of an intermediary orbit for Hyperion’s motion

The motion of Hyperion is an almost perfect application of second kind and second genius orbit, according to Poincaré’s classification. In order to construct such an orbit, we suppose that Titan’s motion is an elliptical one and that the observed frequencies are such that 4n _H−3n _T+3n _ω=0, where n _H, n _T are the mean motions of Hyperion and Titan, n _ω is the rate of rotation of Hyperion’s pericenter. We admit that the observed motion of Hyperion is a periodic motion such as . Then, .N _H, N _T, k∈ N ⁺. With that hypothesis we show that Hyperion’s orbit tends to a particular periodic solution among the periodic solutions of the Keplerian problem, when Titan’s mass tends to zero. The condition of periodicity allows us to construct this orbit which represents the real motion with a very good approximation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Inhomogeneous perfect fluid universe with electromagnetic field

Cylindrically symmetric inhomogeneous cosmological model for perfect fluid distribution with electromagnetic field is obtained. The source of the magnetic field is due to an electric current produced along the z-axis. F ₁₂ is the non-vanishing component of electromagnetic field tensor. To get the deterministic solution, it has been assumed that the expansion θ in the model is proportional to the shear σ. Physical and geometric aspects of the models are also discussed in presence and absence of magnetic field.