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.     

Modified gravity in a viscous and non-isotropic background

We study the dynamical evolution of an f(R) model of gravity in a viscous and anisotropic background which is given by a Bianchi type-I model of the Universe. We find viable forms of f(R) gravity in which one is exactly the Einsteinian model of gravity with a cosmological constant and other two are power law f(R) models. We show that these two power law models are stable with a suitable choice of parameters. We also examine three potentials which exhibit the potential effect of f(R) models in the context of scalar tensor theory. By solving different aspects of the model and finding the physical quantities in the Jordan frame, we show that the equation of state parameter satisfy the dominant energy condition. At last we show that the two power law f(R) models behave like quintessence model at late times and also the shear coefficient viscosity tends to zero at late times.     

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.     

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.     

Evolution of the universe in inverse and lnf(R) gravity

Evolution of the universe is discussed in the framework of f(R) theory of gravity. The deceleration parameter is used to interpret various phases of the universe. We investigate the future evolution of the flat FRW universe by using observationally viable f(R) models. A numerical technique is applied to solve the evolution equation in terms of Hubble parameter which is used to explore late time acceleration of the universe. Some novel and interesting results based on the choice of coupling parameters in gravitational action are obtained. We can conclude that the considered f(R) models imply unification of matter dominated epoch with present accelerating 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.     

Non-vacuum static cylindrically symmetric solution and energy distribution in f(R) gravity

In this paper, we investigate static cylindrically symmetric solution in metric f(R) gravity by taking matter in the form of dust. The assumption of constant Ricci scalar curvature is taken to find the solution. The energy distribution of this solution is explored by applying Landau-Lifshitz energy-momentum complex. In addition, we explore the stability as well as constant scalar curvature conditions for some viable f(R) models along with their energy distribution. It is interesting to mention here that these models satisfy the above mentioned conditions.     

The study of Gödel type solutions in f(R, ϕ) gravity

The aim of this paper is to study the Gödel type universe in modified f(R, ϕ) theory of gravity, where R stands for Ricci scalar and ϕ be the scalar potential. We investigate the modified field equations by using anisotropic and perfect fluid distributions. In particular, we consider two proposed models with some fixed values of parameters and investigate the exact solutions. The behaviour of energy conditions can be seen by a detailed graphical analysis. Furthermore, Tolman-Oppenheimer-Volkoff equation has been studied for both models in this theory. We have also discussed some exact solutions using perfect fluid. It is concluded that f(R, ϕ) theory of gravity support the phenomenon of cosmic expansion of the universe through Gödel type universe for both models.     

Existence of wormhole solutions and energy conditions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

This paper is devoted to investigate the spherically symmetric wormhole models in f(R, T) gravity, where T and R are trace of stress energy tensor and the Ricci scalar, respectively. In this context, we discuss three distinct cases of fluid distributions viz, anisotropic, barotropic and isotropic matter contents. After considering the exponential f(R, T) model, the behavior of energy conditions are analyzed that will help us to explore the general conditions for wormhole geometries in this gravity. It is inferred that the usual matter in the throat could obey the energy conditions but the gravitational field emerging from higher order terms of modified gravity favor the existence of the non-standard geometries of wormholes. The stability as well as the existence of wormholes are also analyzed in this theory.     

Viability bounds in f(R,G) gravity with energy conditions

In the present work, we discuss the viability bounds arising from the energy conditions in the context of an extended gravitational theory namely f(R, G) gravity, where R stands for the curvature scalar and G represents the Gauss-Bonnet invariant. Two specific forms of f(R, G) have been taken into account to examine the validity of the general inequalities obtained by the weak energy condition (WEC). More specifically, we consider the constraints imposed by the weak energy condition (WEC) and verify whether the parameter range of the recent proposed models are consistent with the energy conditions.     

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.     

Dynamics of some cosmological solutions in modified f(R) gravity

This paper is devoted to investigate the modified f(R) theory of gravity, where R represents the Ricci scalar respectively. For our current work, we consider the Friedmann-Robertson-Walker (FRW) space-time for finding solutions of field equations. Furthermore, some numerical solutions are examined by taking the Klein-Gordon Equation and using distinct values of the equation of state (EoS) parameter. In this way, we have discussed the solutions for acceleration expansion of the Universe, sub-relativistic Universe, radiation Universe, ultra-relativistic Universe, dust Universe, and stiff fluid Universe respectively. Moreover, their behaviours are examined by using power-law and exponential law techniques. The bouncing scenario is also discussed by choosing some particular values of the model parameters and observed the energy conditions, which are satisfied for a successful bouncing model. It is also concluded that some solution in f(R) theory of gravity supports the concept of exotic matter and accelerated expansion of the Universe due to a large amount of negative pressure.     

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.     

The unification of the inflation with late-time acceleration in Born-Infeld-f(R) gravity

We study accelerating dynamics from Born-Infeld-f(R) gravity in a simplified conformal approach without matter. In Makarenko et al. (arXiv:1404.2850 [gr-qc], 2011b) it was derived eventually any Dark Energy cosmology from above theory. In this Letter we apply the technique of Makarenko et al. (arXiv:1404.2850 [gr-qc], 2011b) to show that Born-Infeld-f(R) gravity may describe very realistic universe admitting the unification of early-time inflation with late-time acceleration. Specifically, the evolution with periodic as well as non-periodic behavior is considered with possibility to cross the phantom-divide at early or late-times.     

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.     

Thermal relic abundance and anisotropy due to modified gravity

Alternative cosmologies, based on extensions of General Relativity, predict modified thermal histories in the early universe during the pre Big Bang Nucleosynthesis (BBN) era. When the expansion rate is enhanced with respect to the standard case, thermal relics typically decouple with larger relic abundances. In this paper, we study the dynamical evolution of an f(R) model of gravity in a homogeneous and anisotropic background which is given by a Bianchi type-I model of the universe filled with dark matter, which is described by a perfect fluid with a barotropic equation of state. As an example of a consistent analysis of modified gravity, we apply the formalism to a simple background solution of R+βR ⁿ gravity. Our analysis shows that f(R) cosmology allows dark matter masses lesser than 100 GeV, in the regime ρ ^c ?ρ ^m . We finally discuss how these limits apply to some specific realizations of standard cosmologies: an f(R) gravity model, Einstein frame model.     

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.     

Behaviour of physical parameters in extended gravity with hyperbolic function

In this paper, we have constructed the cosmological model of the universe in f(R, T) theory of gravity in a Bianchi type \(\mathrm{VI}_h\) universe for the functional f(R, T) in the form \(f(R,T)=\mu R+\mu T\), where R and T are respectively Ricci scalar and trace of energy momentum tensor and \(\mu \) is a constant. We have made use of the hyperbolic scale factor to find the physical parameters and metric potentials defined in the space-time. The physical parameters are constrained from different representative values to build up a realistic cosmological model aligned with the observational behaviour. The state finder diagnostic pair is found to be in the acceptable range. The energy conditions of the model are also studied.