FRW Cosmological Models with Bulk-Viscosity in?Barber’s Second Self-Creation Theory

We have studied the evolution of spatially homogeneous and isotropic FRW cosmological model with bulk-viscosity in the frame work of Barber’s (Gen. Relativ. Gravit. 14: 117, 1982) second self-creation theory of gravitation. The cosmological models are obtained with the help of special law of variation for Hubble parameter proposed by Bermann (Nuovo Cimento 74B: 182, 1983). Physical parameters of the models have been discussed in case of false vacuum model, Zel’dovich fluid and radiation dominated fluid.     

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.     

A Higher Dimensional Cosmic Domain Wall in Brans-Dicke Theory of Gravitation

Five dimensional Kaluza-Klein Space-time is considered in the presence of thick domain walls in the scalar-tensor theory formulated by Brans and Dicke (Phys. Rev. 124:925, 1961). Exact cosmological model, in this theory, is presented with the help of special law of variation proposed by Berman (Nuovo Cim. B 74:182, 1983) for Hubble’s parameter. Some physical and kinematical properties of the model are also discussed.     

Bianchi Type-III Cosmological Model with Negative Constant Deceleration Parameter in Brans Dicke Theory of Gravitation

Bianchi type-III space time is considered in the presence of perfect fluid source in the scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a cosmological model with negative constant deceleration parameter is obtained in the presence of perfect fluid with disordered radiation. Some physical and kinematical properties of the model are also discussed.     

Lyra’s Cosmology of Massive Strings in Anisotropic Bianchi-II Space-Time

The paper deals with a spatially homogeneous and totally anisotropic Bianchi II cosmological models representing massive strings in normal gauge for Lyra’s manifold. The modified Einstein’s field equations have been solved by applying variation law for Hubble’s parameter. This law generates two type of solutions for average scale factor, one is of power law type and other is of exponential law type. The power law describes the dynamics of Universe from big bang to present epoch while exponential law seems reasonable to project dynamics of future Universe. It has been found that the displacement vector (β) is a decreasing function of time and it approaches to small positive value at late time, which is collaborated with Halford (Aust. J. Phys. 23, 863, 1970) as well as recent observations of SN Ia. The study reveals that massive strings dominate in early Universe and eventually disappear from Universe for sufficiently large time, which is in agreement with the current astronomical observations.     

Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter

The present study deals with a spatially homogeneous and anisotropic Bianchi type-I (B-I) cosmological models representing massive strings in normal gauge for Lyra’s manifold by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. 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-law type. Using these two forms, Einstein’s modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier, P.S.: Phys. Rev. D 28, 2414 (1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component s¹ ₁\sigma^{1}_{~1} of the shear tensor s^j _i\sigma^{j}_{~i}. This condition leads to A=(BC) ^m , where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the both decelerating and accelerating universes. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.     

A Dark Energy Model in a Scale Covariant Theory of Gravitation

An axially symmetric Bianchi type-I space time with variable equation of state (EoS) parameter and constant deceleration parameter has been investigated in scale covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. Some physical and kinematical properties of the model are also discussed.     

LRS Bianchi Type-I Dark Energy Cosmological Model in Brans-Dicke Theory of Gravitation

Bianchi type-I dark energy model with variable equation of state (EoS) parameter is presented in a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). To get a determinate solution of the field equations we will take the help of special law of variation for Hubble’s parameter presented by Bermann (Nuovo Cimento B. 74:182, 1983) which yields a dark energy cosmological model with negative constant deceleration parameter. It is observed that this dark energy cosmological model always represents an accelerated and expanding universe and also consistent with the recent observations of type-Ia supernovae. Some physical and geometrical properties of the model are also discussed.     

On Kantowski-Sachs Cosmic Strings Coupled with Maxwell Fields in Bimetric Relativity

Kantowski-Sachs model is studied with source cosmic cloud strings coupled with electromagnetic field in Rosen’s (Gen. Relativ. Gravit. 4:435, 1973) bimetric theory of relativity. It is shown that there is no contribution from Maxwell fields in this theory. Hence geometric string and vacuum cosmological models are established.     

Magnetized String Cosmology in Anisotropic Bianchi-II Space-time with Variable Cosmological Term-Λ

The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological models representing massive strings 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 energy-momentum tensor for such string as formulated by Letelier (Phys. Rev. D 28:2414, 1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component s¹₁\sigma^{1}_{1} of the shear tensor s^j_i\sigma^{j}_{i}. This condition leads to A=(BC) ^m , where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at present epoch which is in good agreement by the results from recent supernovae observations. Some physical and geometric behaviour of the models are also discussed.     

Bianchi Type VI<Subscript>o</Subscript> Magnetized Anisotropic Dark Energy Models with Constant Deceleration Parameter

The paper deals with an anisotropic Bianchi type VI_o cosmological model with variable ω in the presence and absence of magnetic field of energy density ρ _B . A special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B 74:182, 1983) has been utilized to solve the field equations.     

String Cosmological Solutions in Self-Creation Theory of Gravitation

We have studied the problem of cosmic strings for Bianchi-I, II, VIII and IX string cosmological models in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) second self—creation theory of gravitation. We have obtained some classes of solutions by considering different functional form for metric potentials. It is also observed that due to the presence of scalar field, the power index ‘m’ of the metric coefficients has a range of values.     

Axially Symmetric Cosmological Micro Model in Barber’s Modified Theory of Einstein General Relativity

Axially symmetric Bianchi type-I cosmological micro model is obtained in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) modified theory of general relativity. Some properties of the model are discussed.     

Bianchi Type-I Anisotropic Dark Energy Model with Constant Deceleration Parameter

A new dark energy model in anisotropic Bianchi type-I (B-I) space-time with time dependent equation of state (EoS) parameter and constant deceleration parameter has been investigated in the present paper. The Einstein’s field equations have been solved by applying a variation law for generalized Hubble’s parameter (Berman in Il Nuovo Cimento B 74:182, 1983) which generates two types of solutions, one is of power-law type and other is of the exponential form. The existing range of the dark energy EoS parameter ω for derived model is found to be in good agreement with the three recent observations (i) SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003), (ii) SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004) and (iii) a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type Ia supernovae and galaxy clustering (Hinshaw et al. in Astrophys. J. Suppl. Ser. 180:225, 2009 and Komatsu et al. in Astrophys. J. Suppl. Ser. 180:330, 2009). The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by results from recent supernovae Ia observations. It has also been suggested that the dark energy that explains the observed accelerating universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Geometric and kinematic properties of the model and the behaviour of the anisotropy of the dark energy have been carried out.     

Bianchi Types V and VI<Subscript>0</Subscript> Cosmic Strings Coupled with Maxwell Fields in Bimetric Theory

Spatially homogeneous Bianchi types V and VI₀ cosmological models are studied with source cosmic cloud strings coupled with electromagnetic field in Rosen’s (Gen. Relativ. Gravit. 4:435, 1973) bimetric theory of relativity. It is observed that Bianchi type V space time is feasible whereas Bianchi type VI₀ is not feasible. In the feasible case different equations of state for cosmic strings with Maxwell fields do not survive in this theory and the space-time turns out to be flat.     

A Cosmological Model of Thermodynamic Open Universe

In this paper we have given a generalization of the earlier work by Prigogine et al. (Gen. Relativ. Gravit. 19:1, 1989; Gen. Relativ. Gravit. 21(8):767–776, 1989) who have constructed a phenomenological model of entropy production via particle creation in the very early universe generated out of the vacuum rather than from a singularity, by including radiation also as the energy source and tried to develop an alternative cosmological model in which particle creation prevents the big bang. We developed Radiation dominated model of the universe which shows a general tendency that (i) it originates from instability of vacuum rather than from a singularity. (ii) Up to a characteristic time t _c cosmological quantities like density, pressure, Hubble constant and expansion parameter vary rapidly with time. (iii) After the characteristic time these quantities settles down and the models are turned into de-Sitter type model with uniform matter, radiation, creation densities and Hubble’s constant H. The de-Sitter regime survives during a decay time t _d then connects continuously to a usual adiabatic matter radiation RW universe. The interesting thing in the paper is that we have related the phenomenological radiation dominated model to macroscopic model of quantum particle creation in the early universe giving rise to the present observed value of cosmic background radiation. It is also found that the dust filled model tallies exactly with that of the Prigogine’s one, which justifies that our model is generalized Prigogine’s model. Although the model originates from instability of vacuum rather than from a singularity, still there is a couple of unavoidable singularities in the model.     

String Cloud with Quark Matter in Self-creation Cosmology

We have constructed Bianchi type-III cosmological model with strange quark matter attached to the string cloud in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) second self-creation theory of gravitation which is inflationary. Further it is obtained that the theory leads to Einstein theory at initial epoch and at infinite future.     

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.     

Cylindrically Symmetric Scalar Field and it’s Lyapunov stability in General Relativity

In this paper we found an Exact solution for massless scalar field with cosmological constant. This exact solution generalized the Levi-Civita vacuum solution Levi-Civita (Rend. Acc. Lincei 27:183, 1917) to a massless scalar field, with a cosmological constant term.This solution in the absence of the Cosmological constant recovers the spacetime of a massless scalar field with cylindrical symmetry (Buchdahl metric (Buchdahl in Phys. Rev. 115:1325, 1959)). Also if the scalar field disappears, the spacetime will be a representation of de-Sitter space.We prove that the form of the metric’s function which was purposed in Momeni and Miraghaei (Int. J. Mod. Phys. A 24(31):5991, 2009) is valid even if we assume a general form. Furthermore we show that in which conditions this solution satisfies energy conditions. Finally the credibility of focusing theorem is proved.     

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.