Reconstruction of f(R,T) gravity in anisotropic cosmological models of accelerating universe

In this paper, we search the existence of Bianchi type I cosmological model in f(R,T) gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the trace of the stress-energy tensor T. We obtain the gravitational field equations in the metric formalism, and reconstruct the corresponding f(R,T) functions. Attention is attached to the special case, f(R,T)=f ₁(R)+f ₂(T) and two examples are assumed for this model. In the first example, we consider the unification of matter dominated and accelerated phases with f(R) gravity in anisotropic universe, and in the second instance, model of f(R,T) gravity with transition of matter dominated phase to the acceleration phase is obtained. In both cases, f(R,T) is proportional to a power of R with exponents depending on the input parameters.     

Schwarzschild-NUT solution in modified teleparallel gravity theory

Spherically symmetric tetrad field is applied to the field equation of modified teleparallel gravity theory. Some constraints are assumed on the resulting non-linear partial differential equations. Exact vacuum solution is derived with two constants of integration. The derived solution has a vanishing scalar torsion, i.e., T=T ^μ _νλ S _μ ^νλ =0 and its space-time is axially symmetric. It is shown that this solution can be rewritten as a product of three matrices, two local Lorentz transformations and one diagonal tetrad field. The local Lorentz transformations represent “so(3)” and a boost transformation and the diagonal tetrad reproduce the same metric field of the original tetrad.     

Bianchi type-VI0 perfect fluid cosmological model in a modified theory of gravity

A spatially homogeneous and anisotropic Bianchi type-VI₀ space-time filled with perfect fluid in general relativity and also in the framework of f(R,T) gravity proposed by Harko et al. (in arXiv:1104.2669 [gr-qc], 2011) has been studied with an appropriate choice of the function f(R,T). The field equations have been solved by using the anisotropy feature of the universe in Bianchi type-VI₀ space time. Some important features of the models, thus obtained, have been discussed. We noticed that the involvement of new function f(R,T) doesn’t affect the geometry of the space-time but slightly changes the matter distribution.     

The plane symmetric vacuum solutions of modified field equations in metric f(R) gravity

The f(R) theories of gravity have been interested in recent years. A considerable amount of work has been devoted to the study of modified field equations with the assumption of constant Ricci scalar which may be zero or nonzero. In this paper, the exact vacuum solutions of plane symmetric spacetime are analyzed in f(R) theory of gravity. The modified field equations are studied not only for R=constant but also for general case R≠constant. In particular, we show that the Novotný-Horský and anti-de Sitter spacetimes are the exact solutions of the field equations with the non-zero constant Ricci scalar. Finally, the family of solutions with R≠constant is obtained explicitly which includes the Novotný-Horský, Kottler-Whittaker, Taub and conformally flat spacetimes.     

Gravitational perfect fluid collapse in f(R) gravity

In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric f(R) gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the exterior region of a star. The junction conditions between interior and exterior spacetimes are derived. The field equations in f(R) theory are solved using the assumption of constant Ricci scalar. Inserting their solution into junction conditions, the gravitational mass is found. Further, the apparent horizons and their time of formation is discussed. We conclude that the constant scalar curvature term f(R ₀) acts as a source of repulsive force and thus slows down the collapse of matter. The comparison with the corresponding results available in general relativity indicates that f(R ₀) plays the role of the cosmological constant.     

Functional form of f(R) with power-law expansion in anisotropic model

In this paper, we study an anisotropic Bianchi-I space-time model in f(R) theory of gravity in the presence of perfect fluid as a matter contains. The aim of this paper is to find the functional form of f(R) from the field equations and hence the solution of various cosmological parameters. We assume that the deceleration parameter to be a constant, and the shear scalar proportional to the expansion scalar to obtain the power-law form of the scale factors. We find that the model describes the decelerated phases of the universe under the choice of certain constraints on the parameters. The model does not show the acceleration expansion and also transition from past deceleration to present accelerating epoch. We discuss the stability of the functional form of f(R) and find that it is completely stable for describing the decelerating phase of the universe.     

Generalized teleparallel gravity via some scalar field dark energy models

We consider generalized teleparallel gravity in the flat FRW universe with a viable power-law f(T) model. We construct its equation of state and deceleration parameters which give accelerated expansion of the universe in quintessence era for the obtained scale factor. Further, we develop correspondence of f(T) model with scalar field models such as, quintessence, tachyon, K-essence and dilaton. The dynamics of scalar field as well as scalar potential of these models indicate the expansion of the universe with acceleration in the f(T) gravity scenario.     

Bulk viscous cosmological models in f(R,T) theory of gravity

We have constructed Locally Rotationally Symmetric Bianchi type I (LRSBI) cosmological models in the f(R,T) theory of gravity when the source of gravitation is the bulk viscous fluid. The models are constructed for f(R,T)=R+2f(T) and f(R,T)=f ₁(R)+f ₂(T). We found that in the first case the model degenerates into effective stiff fluid model of the universe. In the second case we obtained degenerate effective stiff fluid model as well as general bulk viscous models of the universe. Some physical and kinematical properties of the models are also discussed.     

Magnetized domain wall in f(R,T) theory of gravity

We studied Bianchi type-V space-time using magnetic domain wall in f(R, T) theory of gravity and deciphered the exact solutions of the corresponding field equations. In this study, we discussed the physical behavior of the resultant cosmological model in the presence and absence of magnetic field with the help of few physical parameters.     

LRS Bianchi type-I cosmological model in f(R,T) theory of gravity

The exact solutions of the field equations in respect of LRS Bianchi type-I space time filled with perfect fluid in the framework of f(R,T) gravity (Harko et al., arXiv: [gr-qc], 2011) are derived. The physical behavior of the model is studied. In fact, the possibility of reconstruction of the LRS Bianchi type-I cosmology with an appropriate choice of a function f(T) has been proved in f(R,T) gravity.     

Study of Bianchi I anisotropic model in f(R,T) gravity

We discuss the Bianchi type I model with perfect fluid as matter content in f(R,T) gravity, where R is the Ricci scalar and T is the trace of the energy-momentum tensor. We obtain exact solutions of the field equations employing the anisotropic feature of spacetime for two expansion laws namely exponential and power expansions. The physical and kinematical quantities are examined for both cases in future evolution of the universe. We also explore the validity of null energy condition and conclude that our solutions are consistent with the current observations.     

Variable Chaplygin gas cosmologies in f(R,T) gravity with particle creation

A flat FLRW (Friedmann–Lemaitre–Robertson–Walker) cosmological model with perfect fluid comprising of variable Chaplygin gas (VCG) has been studied in the context of f(R, T) gravity with particle creation. The solutions of the modified field equations are obtained through three different considered form of scale factors. The effective pressure is negative throughout the evolution of universe, which leads to accelerated expansion of the universe. In addition to that we have also discussed the importance of particle creation pressure on the cosmological parameters, energy conditions and state-finder diagnostic parameters. It is noticed that the time evolution of source function yields almost constant particle production at late times.     

Cosmology of f(T) gravity in a holographic dark energy and nonisotropic background

It is shown that the acceleration of the universe can be understood by considering a f(T) gravity models. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. For these f(T) gravity models, a variant of the accelerating cosmology reconstruction program is developed. We consider spatially homogenous and anisotropic Bianchi type I universe in the context of f(T) gravity. The de Sitter, power-law and general exponential solutions are assumed for the scale factor in each spatial direction and the corresponding cosmological models are reconstructed. We reconstruct f(T) theories from two different holographic dark energy models in different time durations. For the holographic dark energy model, the dark energy dominated era with new setting up is chosen for reconstruction, and the Ricci dark energy model, radiation, matter and dark energy dominated time durations are all investigated. Finally we have obtained a modified gravity action consistent with the holographic dark energy scenario.     

Gravitational energy, momentum and angular momentum of Schwarzschild Anti-de Sitter space-times in the teleparallel equivalent of general relativity

We give a class of spherically symmetric-Anti de Sitter (Ads), exact solution in the teleparallel equivalent of general relativity (TEGR). The solution depends on an arbitrary function F(R)\mathcal{F}(R) and reproduce the metric of Schwarzschild Ads space-time. In the context of the Hamiltonian formulation of the TEGR we compute the gravitational energy of this class. The calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. We show that the form of the energy depends on the arbitrary function. We make a constrain on this arbitrary function to give the correct form of energy.     

Anisotropic cosmological models in f(R,T) gravity according to holographic and new agegraphic dark energy

The paper deals with a spatially homogeneous and anisotropic universe filled with perfect fluid and dark energy components. We consider the f(R,T) theory according to holographic and new agegraphic dark energy in the Bianchi type I universe. In this study, we concentrate on two particular models of f(R,T) gravity namely, R+2f(T) and f(R)+λT. We conclude that the derived f(R,T) models can represent phantom or quintessence regimes of the universe.     

Holographic f(T) gravity model

We try to study the corresponding relation between f(T) gravity and holographic dark energy (HDE). A kind of energy density from f(T) is introduced which has the same role as HDE density. A f(T) model according to the HDE model is calculated. We find out a torsion scalar T based on the scalar factor is assumed by Capoziello et al. (Phys. Lett. B 639:135, 2006). The effective torsion equation of state, deceleration parameter of the holographic f(T)-gravity model are calculated.     

Non-existence of Bianchi type-III bulk viscous string cosmological model in f(R,T) gravity

A spatially homogeneous and anisotropic Bianchi type-III space-time is considered in the presence of bulk viscous fluid containing one dimensional cosmic strings in the frame work of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011). To get a determinate solution of the field equations of this theory, we have used (i) a barotropic equation of state for the pressure and density and (ii) the bulk viscous pressure is proportional to the energy density. It is interesting to observe that, in this case, Bianchi type-III bulk viscous string cosmological model does not exist and degenerates into vacuum model of general relativity.     

Kaluza-Klein universe with cosmic strings and bulk viscosity in f(R,T) gravity

A five dimensional Kaluza-Klein cosmological model is considered in the frame work of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011) when the source for energy momentum tensor is a bulk viscous fluid containing one dimensional cosmic strings. A barotropic equation of state is assumed to get a determinate solution of the field equations. Also, the bulk viscous pressure is assumed to be proportional to the energy density. The physical behavior of the model is also discussed.