Bianchi Type-II String Cosmological Model with Magnetic Field in f (R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of f(R,T) gravity proposed by Harko et al. (Phys Rev D 84:024020, 2011). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento B 74:182, 1983) cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=μ T. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Bianchi Type-II Dark Energy Model in f(R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi Type-II space-time dark energy model with EoS parameter is considered in the presence of a perfect fluid source in the framework of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D, 84:024020, 2011). With the help of special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B, 74:182, 1983) a dark energy cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=λT. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Bianchi Type-V Cosmology in f(R,T) Gravity with Λ(T)

A new class of cosmological models in f(R,T) modified theories of gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011), where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar R and the trace of the stress-energy tensor T, have been investigated for a specific choice of f(R,T)=f ₁(R)+f ₂(T) by considering time dependent deceleration parameter. The concept of time dependent deceleration parameter (DP) with some proper assumptions yield the average scale factor $a(t) = \sinh^{\frac{1}{n}}(\alpha t)$ , where n and α are positive constants. For 0<n≤1, this generates a class of accelerating models while for n>1, the models of universe exhibit phase transition from early decelerating phase to present accelerating phase which is in good agreement with the results from recent astrophysical observations. Our intention is to reconstruct f(R,T) models inspired by this special law for the deceleration parameter in connection with the theories of modified gravity. In the present study we consider the cosmological constant Λ as a function of the trace of the stress energy-momentum-tensor, and dub such a model “Λ(T) gravity” where we have specified a certain form of Λ(T). Such models may display better uniformity with the cosmological observations. The statefinder diagnostic pair {r,s} parameter has been embraced to characterize different phases of the universe. We also discuss the physical consequences of the derived models.     

Kantowski-Sachs Universe Filled with Perfect Fluid in f(R,T) Theory of Gravity

The exact solutions of the field equations in respect of Kantowski-Sachs universe filled with perfect fluid in the framework of f(R,T) theory of gravity (Harko et al. in Phys. Rev. D 84:024020, 2011) is derived. A cosmological model with an appropriate choice of the function f(T) is constructed. The physical behavior of the cosmological model is studied. Some important features of astrophysical phenomena, like Hubble’s parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with red-shift are also discussed.     

The simplest non-minimal matter–geometry coupling in the <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) cosmology

f(R, T) gravity is an extended theory of gravity in which the gravitational action contains general terms of both the Ricci scalar R and the trace of the energy-momentum tensor T. In this way, f(R, T) models are capable of describing a non-minimal coupling between geometry (through terms in R) and matter (through terms in T). In this article we construct a cosmological model from the simplest non-minimal matter–geometry coupling within the f(R, T) gravity formalism, by means of an effective energy-momentum tensor, given by the sum of the usual matter energy-momentum tensor with a dark energy contribution, with the latter coming from the matter–geometry coupling terms. We apply the energy conditions to our solutions in order to obtain a range of values for the free parameters of the model which yield a healthy and well-behaved scenario. For some values of the free parameters which are submissive to the energy conditions application, it is possible to predict a transition from a decelerated period of the expansion of the universe to a period of acceleration (dark energy era). We also propose further applications of this particular case of the f(R, T) formalism in order to check its reliability in other fields, rather than cosmology.     

Quark and strange quark matter in f(R) gravity for Bianchi type I and V space-times

Behaviors of quark matter and strange quark matter which exist in the first seconds of the early Universe in f(R) gravity are studied for Bianchi I and V universes. In this respect, we obtain exact solutions of the modified Einstein field equations by using anisotropy feature of Bianchi I and V space-times. In particular, we investigate exact f(R) functions for Bianchi I as the contribution of strange quark and quark matter. Also, we have concluded that quark matter may contribute to the early acceleration of the universe since quark matter behaves like phantom-type dark energy. Furthermore, obtained f(R) solutions represents early eras of the Universe since f(R) solutions for quark matter coincide with f(R) equations for inflation. From this point, we can reach the conclusion that quarks may be source of the early dark energy of the universe or source of little inflation due to their repulsive force.     

Late-time cosmological approach in mimetic <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

In this paper, we investigate the late-time cosmic acceleration in mimetic f(R, T) gravity with the Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations the main equation that can describe the cosmological evolution. Then, with several models from \(\mathcal {Q}(z)\) and the well-known particular model f(R, T), we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and in each case we compare the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic f(R, T) gravity. The results obtained are in good agreement with the observational data and show that in the presence of the collisional matter the dark energy oscillations in mimetic f(R, T) gravity can be damped.     

Reconstruction of some cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) cosmology

In this paper, we reconstruct cosmological models in the framework of f(R,T) gravity, where R is the Ricci scalar and T is the trace of the stress-energy tensor. We show that the dust fluid reproduces ΛCDM, phantom–non-phantom era and phantom cosmology. Further, we reconstruct different cosmological models, including the Chaplygin gas, and scalar field with some specific forms of f(R,T). Our numerical simulation for the Hubble parameter shows good agreement with the BAO observational data for low redshifts, z<2.     

Spatially Homogeneous Rotating Solution in f(R) Gravity and Its Energy Contents

In this paper, the metric approach of f(R) theory of gravity is used to investigate the exact vacuum solutions of spatially homogeneous rotating spacetimes. For this purpose, R is replaced by f(R) in the standard Einstein-Hilbert action and the set of modified Einstein field equations reduce to a single equation. We adopt the assumption of constant Ricci scalar which maybe zero or non-zero. Moreover, the energy density of the non-trivial solution has been evaluated by using the generalized Landau-Lifshitz energy-momentum complex in the perspective of f(R) gravity for some appropriate f(R) model, which turns out to be a constant quantity.     

Bianchi V cosmological model in Palatini <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We apply the dynamical systems approach to investigate the spatially homogeneous and anisotropic Bianchi type V models for the Palatini version of f(R) gravity. In particular, we examine the existence of equilibrium points along with their exact solutions and stability properties for two different forms of f(R). Moreover, the evolution of shear and spatial curvature by performing the phase space analysis are studied and also the phases of evolution from anisotropic universe to the stable de-Sitter flat universe are discussed.     

Hypersurface-homogeneous Universe filled with perfect fluid in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) theory of gravity

The exact solutions of the field equations with respect to hypersurface-homogeneous Universe filled with perfect fluid in the framework of f(R, T) theory of gravity (Harko et al, Phys. Rev. D 84, 024020 (2011)) is derived. The physical behaviour of the cosmological model is studied.     

Magnetized strange quark matter solutions in f(R,T) gravity with cosmological constant

In this research, we have studied magnetized strange quark matter (SQM) solutions for Friedmann-Robertson-Walker (FRW) universe in f(R, T) gravity. To obtain exact solutions of modified field equations we have used $f(R,T)=R+2f\left(T\right)$ and $f(R,T)=f_1\left(R\right)+f_2\left(T\right)$ models given by Harko et al. (Harko et al. in Phys. Rev. D 84:024020, 2011) and $f(R,T)=R+f_3\left(T\right)$ model (here f₃ is an arbitrary function) with cosmological constant Λ. For t → ∞ we obtain $p=?\rho$ dark energy situation with small constant values of cosmological constant in three different f(R, T) gravitation models. In our solutions magnetic field does not observe also we have transformed our solutions from FRW universe to Static Einstein Universe (SEU) and we get f(R, T) gravity results for SEU universe. Finally we discussed our physical solutions.     

Exploring plane-symmetric solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane-symmetric solutions in the context of metric f(R) gravity. We extend the work on static plane-symmetric vacuum solutions in f(R) gravity already available in the literature [1, 2]. The modified field equations are solved using the assumptions of both constant and nonconstant scalar curvature. Some well-known solutions are recovered with power-law and logarithmic forms of f(R) models.     

Higher Dimensional Cosmological Models Filled with Perfect Fluid in f(R,T) Theory of Gravity

The new class of higher dimensional cosmological model of the early universe filled with perfect fluid source in the framework of f(R,T) theory of gravity (Harko et al. in Phys. Rev. D 84, 024020, 2011) is considered. A cosmological model with an appropriate choice of the function f(T) has been constructed. The physical behavior of the model is studied. The well known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with redshift are discussed.     

Friedmann Cosmology with Matter Creation in Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

The theoretical and observational consequences of thermodynamics of open systems which allow matter creation, are investigated in modified f(R, T) (R is the Ricci scalar and T is the trace of energy-momentum tensor) theory of gravity within the framework of a flat Friedmann-Robertson-Walker line element. The simplest model f(R, T)=R+2f(T) with “gamma-law” equation of state p = (γ?1)ρ is assumed to obtain the exact solution. A power-law expansion model is proposed by considering the natural phenomenological particle creation rate ψ = 3β n H, where β is a pure number of the order of unity, n the particle number density and H is the Hubble parameter. A Big Rip singularity is observed for γ<0 describing phantom cosmology. The accelerated expansion of the Universe is driven by the particle creation. The density parameter shows the negative curvature of the Universe due to particle creation. The entropy increases with the evolution of the Universe. Some kinematics tests such as lookback time, luminosity distance, proper distance, angular diameter versus redshift are discussed in detail to observe the role of particle creation in early and late time evolution of the Universe.     

Noncommutative Wormholes in f(R) Gravity with Lorentzian Distribution

In this paper, we derive some new exact solutions of static wormholes in f(R) gravity supported by the matter possesses Lorentzian density distribution of a particle-like gravitational source. We derive the wormhole’s solutions in two possible schemes for a given Lorentzian distribution: assuming an astrophysically viable F(R) function such as a power-law form and discuss several solutions corresponding to different values of the exponent (here $F =\frac{df}{dR}$ ). In the second scheme, we consider particular form of two shape functions and have reconstructed f(R) in both cases. We have discussed all the solutions with graphical point of view.     

Dynamics of anisotropic power-law <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) cosmology

Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f(R) theory has been investigated extensively due to important f(R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f(R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f(R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f(R) gravity supports the crucial issue of accelerated expansion of the universe.     

Cosmology from <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) Theory in a Variant Speed of Light Scenario

In this work I present a generalization of f(R, T) gravity, by allowing the speed of light to vary. Cosmological solutions are presented for matter and radiation-dominated universes, the former allowing the universe expansion to accelerate while the latter contemplating a possible alternative to inflationary scenario. Remarkably, standard gravity is always retrieved for a special case of f(R, T).     

Vacuum spherically symmetric solutions in f(T) gravity

Spherically symmetric static vacuum solutions have been built in f(T) models of gravity theory. We apply some conditions on the metric components; then new vacuum spherically symmetric solutions are obtained. Also, by extracting metric coefficients we determine the analytical form of f(T).     

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.