Non-static plane symmetric cosmological models in bimetric theory

The problems of non-static plane symmetric meson field and mesonic perfect fluid in Rosen’s [Gen. Rel. Grav., Vol. 4 (1973) 435] bimetric theory of gravitation are considered. It is observed that plane symmetric non-static cosmological model exists in case of scalar meson field where the scalar field becomes constant. Further it is found that in case of mesonic perfect fluid, the bimetric theory does not admit perfect fluid but allows only mesonic scalar field with constant scalar field. In both the cases a cosmological model with constant scalar field is obtained.     

Bianchi Type-I Space-Time with Variable Cosmological Constant

A spatially homogeneous and anisotropic Bianchi type-I perfect fluid model is considered with variable cosmological constant. Einstein’s field equations are solved by using a law of variation for mean Hubble’s parameter, which is related to average scale factor and that yields a constant value of deceleration parameter. An exact and singular Bianchi-I model is presented, where the cosmological constant remains positive and decreases with the cosmic time. It is found that the solutions are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the model is carried out.     

Cosmological models with constant deceleration parameter in Nordtvedt’s theory

Exact solutions of the field equations of Nordtvedt’s theory for spatially flat FRW models with constant deceleration parameter have been obtained. Singular solutions with (i) power-law (ii) exponential expansion have been studied in Nordtvedt’s theory where the coupling parameterω is a function of the scalar fieldφ.     

Some Exact Bianchi Type V Perfect Fluid Solutions with Heat Flow

The variation law for generalized mean Hubble’s parameter is discussed in a spatially homogeneous and anisotropic Bianchi type V space-time with perfect fluid along with heat-conduction. The variation law for Hubble’s parameter, that yields a constant value of deceleration parameter, generates two types of solutions for the average scale factor, one is of power-law type and other one of exponential form. Using these two forms of the average scale factor, exact solutions of Einstein field equations with a perfect fluid and heat conduction are presented for a Bianchi type V space-time, which represent expanding singular and non-singular cosmological models. We find that the constant value of deceleration parameter is reasonable for the present day universe. The physical and geometrical properties of the models are also discussed in detail.     

Some Exact Bianchi Type-V Perfect Fluid Cosmological Models with Heat Flow and Decaying Vacuum Energy Density Λ: Expressions for Some Observable Quantities

In this paper we have obtained some new exact solutions of Einstein’s field equations in a spatially homogeneous and anisotropic Bianchi type-V space-time with perfect fluid distribution along with heat-conduction and decaying vacuum energy density Λ by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein’s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The cosmological constant Λ is found to be a decreasing function of time and positive which is corroborated by results from recent supernovae Ia observations. Expressions for look-back time-redshift, neoclassical tests (proper distance d(z)), luminosity distance red-shift and event horizon are derived and their significance are described in detail. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Exact self-consistent plane-symmetric solutions of the equations of two interacting fields (spinor field and scalar field)

A spinor field interacting with a zero-mass neutral scalar field is considered for the case of the simplest type of direct interaction, where the interaction Lagrangian has the formL _int =1/2 ϕ_αϕ_,α F(S) whereF(S) is an arbitrary function of the spinor field invariantS=ψψ. Exact solutions of the corresponding systems of equations that take into account the natural gravitational field in a plane-symmetric metric are obtained. It is proved that the initial system of equations has regular localized soliton-type solutions only if the energy density of the zero-mass scalar field is negative as it “disengages” from interaction with the spinor field. In two-dimensional space-time the system of field equations we are studying describes the configuration of fields with constant energy densityT ₀₀ , i.e., no soliton-like solutions exist in this case. Russian People’s Friendship University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 69–75, July, 1998.     

Higher dimensional Vaidya metric in Einstein and de Sitter background

Spherically symmetric non-static higher dimensional metrics are considered in connection with Einstein’s field equations. Two exact solutions are derived. One of them corresponds to a mixture of perfect fluid and pure radiation field and represents higher dimensional Vaidya metric in the cosmological background of Einstein static universe. The other corresponds to a pure radiation field and represents higher dimensional Vaidya metric in the background de Sitter universe. For both of these solutions, the cosmological constant is taken to be non-zero. Many known solutions are derived as particular cases.     

Exact Bianchi Type-I Cosmological Models in a Scalar-Tensor Theory

In this paper, a spatially homogeneous and anisotropic Bianchi type-I space-time filled with perfect fluid is investigated within the framework of a scalar-tensor theory proposed by Saez and Ballester. 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. One of the models is found to generalize a model recently investigated by Reddy et al. (Astrophys. Space Sci. 306:171, 2006). The Einstein’s field equations are solved exactly and the solutions are found to be consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the models is carried out.     

Cosmological constant in the Bianchi type-I-modified Brans-Dicke cosmology

In 1961, Brans and Dicke [1] provided an interesting alternative to general relativity based on Mach’s principle. To understand the reasons leading to their field equations, we first consider homogeneous and isotropic cosmological models in the Brans-Dicke theory. Accordingly we start with the Robertson-Walker line element and the energy tensor of a perfect fluid. The scalar field φ is now a function of the cosmic time only. Then we consider spatially homogeneous and anisotropic Bianchi type-I-cosmological solutions of modified Brans-Dicke theory containing barotropic fluid. These have been obtained by imposing a condition on the cosmological parameter Λ(φ). Again we try to focus the meaning of this cosmological term and to relate it to the time coordinate which gives us a collapse singularity or the initial singularity. On the other hand, our solution is a generalization of the solution found by Singh and Singh [2]. As far as we are aware, such solution has not been given earlier.     

Bulk viscous cosmology in early Universe

The effect of bulk viscosity on the early evolution of Universe for a spatially homogeneous and isotropic Robertson-Walker model is considered. Einstein’s field equations are solved by using ‘gamma-law’ equation of state p = (γ − 1)ρ, where the adiabatic parameter gamma (γ) depends on the scale factor of the model. The ‘gamma’ function is defined in such a way that it describes a unified solution of early evolution of the Universe for inflationary and radiation-dominated phases. The fluid has only bulk viscous term and the coefficient of bulk viscosity is taken to be proportional to some power function of the energy density. The complete general solutions have been given through three cases. For flat space, power-law as well as exponential solutions are found. The problem of how the introduction of viscosity affects the appearance of singularity, is briefly discussed in particular solutions. The deceleration parameter has a freedom to vary with the scale factor of the model, which describes the accelerating expansion of the Universe.      

Pryce-Hoyle Tensor in a Combined Einstein-Cartan-Brans-Dicke Model

In addition to introducing matter injection through a scalar field determined by Pryce-Hoyle tensor, we also combine it with a BCDE (Brans-Dicke-Einstein-Cartan) theory with lambda-term developed earlier by Berman (Astrophys. Space Sci. 314:79–82, 2008), for inflationary scenario. It involves a variable cosmological constant, which decreases with time, jointly with energy density, cosmic pressure, shear, vorticity, and Hubble’s parameter, while the scale factor, total spin and scalar field increase exponentially. The post-inflationary fluid resembles a perfect one, though total spin grows, but not the angular speed (Berman, in Astrophys. Space Sci. 312:275, 2007). The Pryce-Hoyle tensor, which can measured by the number of injected particles per unit proper volume and time, as well as shear and vorticity, can be neglected in the aftermath of inflation (“no-hair”).     

A Cosmological Model with Negative Constant Deceleration Parameter in a General Scalar-Tensor Theory of Gravitation

Spatially homogeneous and anisotropic LRS Bianchi type-I metric is considered in the framework of Nordtvedt-Barker’s general scalar-tensor theory of gravitation when the source for the energy momentum tensor is a perfect fluid. With the help of a special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cim. B. 74:182, 1983) a cosmological model with negative constant deceleration parameter is obtained. Some physical and kinematical properties of the model are also discussed.     

Standstill Electric Charge Generates Magnetostatic Field under Born-Infeld Electrodynamics

The Abelian Born-Infeld classical non-linear Electrodynamic has been used to investigate the electric and magnetostatic fields generated by a point-like electric charge at rest in an inertial frame. The results show a rich internal structure for the charge. Analytical solutions have also been found. Such fields configurations have been interpreted in terms of vacuum polarization and magnetic-like charges produced by the very high strengths of the electric field considered. Apparently non-linearity is responsible for the emergence of an anomalous magnetostatic field suggesting a possible connection to that created by a magnetic dipole composed of two magnetic charges with opposite signs. Consistently in situations where the Born-Infeld field strength parameter is free to become infinite, Maxwell’s regime takes over, the magnetic sector vanishes and the electric field assumes a Coulomb behavior with no trace of a magnetic component. The connection to other monopole solutions, like Dirac’s and ’tHooft’s Poliakov’s types are also discussed. Finally, some speculative remarks are presented in an attempt to explain such fields.     

Static perfect fluids with Pant-Sah equations of state

We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein’s equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and “rediscovered” by Rosquist and by the present author. Except for the Buchdahl solutions which are contained as a limiting case, the fluids have finite radius and are physically realistic for suitable parameter ranges. The equations of state can be characterized geometrically by the property that the 3-metric on the static slices, rescaled conformally with the fourth power of any linear function of the norm of the static Killing vector, has constant scalar curvature. This local property does not require spherical symmetry; in fact it simplifies the proof of spherical symmetry of asymptotically flat solutions which we recall here for the Pant-Sah equations of state. We also consider a model in Newtonian theory with analogous geometric and physical properties, together with a proof of spherical symmetry of the asymptotically flat solutions. Supported by grants FIS2006-05319 (Ministerio de Educación y Tecnología) and SA010C0 (Junta de Castillia y León).     

Anisotropic Bulk Viscous Fluid Cosmological Model with Zero-Rest-Mass Scalar Field and Time-Dependent Cosmological Term

In this paper, we have investigated Bianchi type-III cosmological model in the presence of a bulk viscous fluid together with zero-rest-mass scalar field and time-dependent cosmological term. We have shown that the field equations are solvable for any arbitrary cosmic scale function. Exact solutions of Einstein’s field equations are obtained which represent an expanding, shearing, non-rotating and decelerating model of the universe. Some physical and geometrical behaviours of the cosmological model are discussed.     

Bianchi-I Space-time with Variable Gravitational and?Cosmological “Constants”

We consider Einstein’s field equations with variable gravitational and cosmological “constants” for a spatially homogeneous and anisotropic Bianchi-I space-time. A law of variation for the Hubble parameter, which is related to the average scale factor and yields a constant value of the deceleration parameter, is assumed to solve the field equations. The gravitational constant is allowed to follow a power-law form. We find that a time-increasing gravitational constant is suitable for describing the present evolution of universe. The solutions reveal the dynamics of a universe, which expands forever. The physical interpretation of the solutions is discussed in detail.     

A New Class of Inhomogeneous Cosmological Models with Electromagnetic Field in Normal Gauge for Lyra’s Manifold

A new class of exact solutions of Einstein’s modified field equations in inhomogeneous space-time for perfect fluid distribution with electromagnetic field is obtained in the context of normal gauge for Lyra’s manifold. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F ₁₂ is a non-vanishing component of the electromagnetic field tensor. It has been found that the displacement vector β(t) behaves like the cosmological constant Λ in the normal gauge treatment and the solutions are consistent with the recent observations of Type Ia supernovae. Physical and geometric aspects of the models are also discussed in the presence of magnetic field.     

An isotropic cosmological model in general scalar tensor theory

An isotropic homogeneous cosmological model with Robertson-Walker line element is studied in general scalar tensor theory where the parameterω is a function of the scalar field. The model consists of perfect fluid with the equation of statep=ερ. Exact solutions are obtained in Dicke’s conformally transformed units forε=1 andε=1/3 assuming a functional relationship betweenω and the scalar fieldφ. The properties are compared with vacuum models in this theory.     

Scalar field dynamics on a brane

The dynamics of a flat isotropic brane Universe with two-component matter source —perfect fluid with the equation of statep = (γ − 1)ρ and a scalar field with a power-law potentialV ∼ φ^α is investigated. We describe solutions for which the scalar field energy density scales as a power-law of the scale factor. We also describe solutions existing in regions of the parameter space where these scaling solutions are unstable or do not exist.     

Noether symmetry for Gauss–Bonnet dilatonic gravity

Noether symmetry for Gauss–Bonnet Dilatonic interaction exists for a constant dilatonic scalar potential and a linear functional dependence of the coupling parameter on the scalar field. The symmetry with the same form of the potential and coupling parameter exists all in the vacuum, radiation and matter dominated era. The late time acceleration is driven by the effective cosmological constant rather than the Gauss–Bonnet term, while the later compensates for the large value of the effective cosmological constant giving a plausible answer to the well-known coincidence problem.