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.     

Magnetized cosmological models in bimetric theory of gravitation

Bianchi type-III magnetized cosmological model when the field of gravitation is governed by either a perfect fluid or cosmic string is investigated in Rosen’s [1] bimetric theory of gravitation. To complete determinate solution, the condition, viz., A=(BC) ⁿ , where n is a constant, between the metric potentials is used. We have assumed different equations of state for cosmic string [2] for the complete solution of the model. Some physical and geometrical properties of the exhibited model are discussed and studied.     

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.     

Kaluza-Klein Cosmological Model in f(R,T) Gravity

A five dimensional Kaluza-Klein space-time is considered in the presence of perfect fluid source in f(R,T) gravity proposed by Harko et al. ( [gr-qc], 2011). A cosmological model with a negative constant deceleration parameter with an appropriate choice of a function f(T) is presented. To find a determinate solution of the field equations it is assumed that scalar of expansion is proportional to the shear scalar of the space time. The physical behavior of the model is also studied.     

Tilted LRS Bianchi Type-I Mesonic Stiff Fluid Cosmological Model

Tilted LRS Bianchi type-I cosmological model for perfect fluid distribution coupled with zero–mass scalar field is investigated. Exact solutions to the field equations are derived when the metric potentials are functions of cosmic time only. Some physical and geometrical properties of the solutions are also discussed.     

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.     

Anisotropic Plane Symmetric Magnetized Model with Cosmological Constant

In this paper, we have obtained the solutions of perfect fluid cosmological model in Cylindrically-symmetric space time (Marder in Proc. R. Soc. A 246:133, 1958) with varying cosmological constant in the presence of electromagnetic field. To get determinate model of the universe we assumed that the scalar of expansion in the model is proportional to the eigen-value of the shear tensor which lead to the condition A=(BC) ⁿ . The magnetic field is due to an electric current produced along x-axis. Thus the magnetic field is in yz-plane and F ₂₃ is the only non-vanishing component of electromagnetic field tensor F _ij . Various physical and geometrical features of the model have been discussed.     

Cosmological analysis of scalar field models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

This paper determines the existence of Noether symmetry in non-minimally coupled f(R, T) gravity admitting minimal coupling with scalar field models. We consider a generalized spacetime which corresponds to different anisotropic and homogeneous universe models. We formulate symmetry generators along with conserved quantities through Noether symmetry technique for direct and indirect curvature–matter coupling. For dust and perfect fluids, we evaluate exact solutions and construct their cosmological analysis through some cosmological parameters. We conclude that decelerated expansion is obtained for the quintessence model with a dust distribution, while a perfect fluid with dominating potential energy over kinetic energy leads to the current cosmic expansion for both phantom as well as quintessence models.     

Abelian cosmic string in the extended Starobinsky model of gravity

We analyze numerically the behaviour of the solutions corresponding to an Abelian cosmic string taking into account an extension of the Starobinsky model, where the action of general relativity is replaced by \(f(R) = R - 2\Lambda + \eta R^2 + \rho R^m\), with \(m > 2\). As an interesting result, we find that the angular deficit which characterizes the cosmic string decreases as the parameters \(\eta \) and \(\rho \) increase. We also find that the cosmic horizon due to the presence of a cosmological constant is affected in such a way that it can grows or shrinks, depending on the vacuum expectation value of the scalar field and on the value of the cosmological constant.     

The Decay of Massive Scalar Field in Non-Static Gödel Type Universe with Viscous Fluid and Heat Flow

In this study, we have investigated the dynamics of non-static Gödel type rotating universe with massive scalar field, viscous fluid and heat flow in the presence of cosmological constant. For various cosmic matter forms, the behavior of the cosmological constant (Λ), shear (η) and bulk (ξ) viscosity coefficients and other kinematic quantities have studied in the early universe. We have showed the decay of massive scalar field in the non-static rotating Gödel type universe and we have obtained constant scalar field with and without source density. Also, we have investigated the effects of massive scalar field on the matter density and pressure. From solutions of the field equations, we have a cosmological model with non-zero expansion, shear, heat flux and rotation. Also some physical and geometrical aspects of the model discussed.     

Magnetized Bianchi Type III String Universe with Time Decaying Vacuum Energy Density Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 28:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. It is observed that the particle density and the tension density of the string are comparable at the two ends and they fall off asymptotically at similar rate. But in early stage as well as at the late time of the evolution of the universe we have two types of scenario (i) universe is dominated by massive strings and (ii) universe is dominated by strings depending on the nature of the two constants L and ℓ. The value of cosmological constant Λ for the model is found to be small and positive which is supported by the results from recent supernovae Ia observations. Some physical and geometric properties of the model are also discussed.     

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 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.     

Bianchi type-I massive string magnetized barotropic perfect fluid cosmological model in bimetric theory

Bianchi type-I massive string cosmological model for perfect fluid distribution in the presence of magnetic field is investigated in Rosen’s [Gen. Relativ. Gravit. 4, 435 (1973)] bimetric theory of gravitation. To obtain the deterministic model in terms of cosmic time, we have used the condition A = (BC) ⁿ , where n is a constant, between the metric potentials. The magnetic field is due to the electric current produced along the x-axis with infinite electrical conductivity. Some physical and geometrical properties of the exhibited model are discussed and studied.     

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.     

Ab-initio calculations of electric field gradient in Ru compounds and their implication on the nuclear quadrupole moments of $$^{99}\hbox {Ru}$$ and $$^{101}\hbox {Ru}$$101Ru

We study a spatially homogeneous and anisotropic cosmological model in the Einstein gravitational theory with a minimally coupled scalar field. We consider a non-interacting combination of scalar field and perfect fluid as the source of matter components which are separately conserved. The dynamics of cosmic scalar fields with a zero rest mass and an exponential potential are studied, respectively. We find that both assumptions of potential along with the average scale factor as an exponential function of scalar field lead to the logarithmic form of scalar field in each case which further gives power-law form of the average scale factor. Using these forms of the average scale factor, exact solutions of the field equations are obtained to the metric functions which represent a power-law and a hybrid expansion, respectively. We find that the zero-rest-mass model expands with decelerated rate and behaves like a stiff matter. In the case of exponential potential function, the model decelerates, accelerates or shows the transition depending on the parameters. The isotropization is observed at late-time evolution of the Universe in the exponential potential model.     

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.     

FRW Cosmological Solution in Self Creation Theory

In this paper, we have investigated spatially homogeneous isotropic Friedman-Robertson-Walker cosmological model with bulk viscosity and zero-mass scalar field in the frame work of Barber’s second self-creation theory (Gen. Relativ. Gravit. 14:117, 1982). The cosmological models are obtained with the help of the special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento B 74:182, 1983) and power law relation. Some physical properties of the models are also discussed.     

Charged perfect fluids in the presence of a cosmological constant

We consider the static and spherically symmetric field equations of general relativity for charged perfect fluid spheres in the presence of a cosmological constant. Following work by Florides (J Phys A Math Gen 16:1419–1433, 1983) we find new exact solutions of the field equations, and discuss their mass radius ratios. These solutions, for instance, require the charged Nariai metric to be the vacuum part of the spacetime. We also find charged generalizations of the Einstein static universe and speculate that the smallness problem of the cosmological constant might become less problematic if charge is taken into account.     

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.