Phantom and Quintessence Fields Coupled to Scalar Curvature in General <i>f(R)</i>Gravity Theory

This paper reviews the development of f(R) gravity theory and Phantom and Quintessence fields. Specifically, we present a new general action of f(R) gravity and Phantom and Quintessence fields coupled to scalar curvature. Then, we deduce Euler-Lagrange Equations of different fields, matter tensor and effective matter tensor. Additionally, this paper obtains the general pressure, density and speed sound of the new general field action, and investigates different cosmological evolutions with inflation. Further, this paper investigates a general f(R) gravity theory with a general matter action and obtains the different field equations, general matter tensor and effective matter tensor. Besides, this paper obtains the effective Strong Energy Condition (SEC) and effective Null Energy Condition (NEC). Then, we prove that when f(R) approaches to R, the effective SEC and the effective NEC approach to the usual SEC and the usual NEC, respectively. Finally, this paper presents a general action of f(R) gravity, Quintessence and Phantom fields and their applications.

Late Time Behavior of the Cosmological Model in Modified Theory of Gravity

We report a viable exponential gravity model for the accelerated expansion of the universe in Bianchi VIh space-time. By considering the estimated physical parameters, the cosmological models are constructed and analyzed in detail. We found that the state parameter in both the models increases to a higher negative range in an early epoch of the phantom domain and it goes to the positive domain at a late phase of the evolution. The effective cosmological constant remains in a positive domain for both models, which is a good sign of accelerating expansion of the universe.

Stability of LRS Bianchi type-I cosmological models in f(R,T)-gravity

This paper examines the stability of the transition from the early decelerating stage of the Universe to the recent accelerating stage for the perfect fluid cosmological locally rotationally symmetric(LRS) Bianchi-I model in f(R, T) theory. To determine the solution of field equations, the idea of a timevarying deceleration parameter(DP) which yields a scale factor, for which the Universe attains a phase transition scenario and is consistent with recent cosmological observations, is used. The time-dependent DP yields a scale factor a=exp■, where β and k are respectively arbitrary and integration constants. By using the recent cons_traints(H_0 _= 73.8, and q_0 =-0.54) from Type Ia Supernova(SN Ia) data in combination with Baryonic Acoustic Oscillations(BAO) and Cosmic Microwave Background(CMB) observations(Giostri et al.), we obtain the values of β = 0.0062 and k = 0.000016 for which we have derived a cosmological model from the early decelerated phase to the present accelerating phase. By applying_ other r_ecent constraints(H_0 = 73.8, q_0 =-0.73) from SNe Ia Union data(Cunha), we obtain the values of β = 0.0036 and k = 0.000084 for which we have derived a cosmological model in the accelerating phase only. We have compared both models with experimental data. The stability of the background solution has been examined also for the metric perturbations alongside the properties of future singularities in a Universe ruled by dark energy with phantom type fluid. We demonstrate the presence of a stable fixed point with a condition of state ω <-1 and numerically affirm this is really a late-time attractor in the ghost overwhelmed Universe. Some physical and geometric properties of the model are found and examined.

Magnetic Field of a Compact Spherical Star under f(R,T) Gravity

We present the interior solutions of distributions of magnetized fluid inside a sphere in f（R, T） gravity. Tile magnetized sphere is embedded in an exterior Reissner NordstrOm metric. We assume that all physical quantities are in static equilibrium. The perfect fluid matter is studied under a particular form of the Lagrangian density f（R, T）. The magnetic field profile in modified gravity is calculated. Observational data of neutron stars are used to plot suitable models of magnetized compact objects. We reveal the effect of f（R, T） gravity on the magnetic field profile, with application to neutron stars, especially highly magnetized neutron stars found in x-ray pulsar systems. Finally, the effective potential Veff and innermost stable circular orbits, arising out of the motion of a test particle of negligible mass influenced by attraction or repulsion from the massive center, are discussed.

Dynamics of Bianchi I Universe in Extended Gravity with Scale Factors

In this paper, the dynamical behavior of an anisotropic universe in an extended gravity e.g. the f (R,T ) theory of gravity is studied. We use f (R,T ) = R + 2μT , where R is the Ricci scalar, T is the trace of energy-momentum tensor and μ is a constant. Two cosmological models are constructed using the power law expansion and hybrid law cosmology in Bianchi type I universe, where the matter field is considered to be a perfect fluid. It is found that in both the cases the anisotropic behavior is in agreement with the observational results. The state finder diagnostic pair and energy conditions are also calculated and analyzed.

Time Varying Deceleration Parameter in <i>f</i>(<i>R</i>, <i>T</i>) Gravity

In the present study, a homogeneous and anisotropic LRS Bianchi type I universe model is considered in f(R, T) theory of gravity. In order to find an exact solution of the field equations of the model, the model presented is based on a unique condition of periodically time varying deceleration parameter. The physical and geometrical characteristics of the universe model have been studied. It has been shown that the model has point-type singularity and all the cosmological parameters possess periodic time behavior. The model has a cyclic expansion history, for example, the model starts with the decelerating expansion, and later it transits to an accelerating phase of expansion and then goes to super-exponential phase of expansion in a period.

Non-static plane symmetric perfect fluid solutions and Killing symmetries in f(R,T)gravity

In this paper,the non-static solutions for perfect fluid distribution with plane symmetry in f(R,T)gravitational theory are obtained.Firstly,using the Lie symmetries,symmetry reductions are performed for considered vector fields to reduce the number of independent variables.Then,corresponding to each reduction,exact solutions are obtained.Killing vectors lead to different conserved quantities.Therefore,we figure out the Killing vector fields corresponding to all derived solutions.The derived solutions are further studied and it is observed that all of the obtained spacetimes,at least admit to the minimal symmetry group which consists of δ_(y),δ_(z) and -zδ_(y)+yδ_(z).The obtained metrics,admit to 3,4,6,and 10,Killing vector fields.Conservation of linear momentum in the direction of y and z,and angular momentum along the x axis is provided by all derived solutions.

f(R)引力理论及其解的研究

首先介绍了f(R)引力理论的发展,然后引入了f(R)引力度规形式及引力场方程,重点分析了f(R)引力理论与标量—张量理论及其联系.最后我们推导了度规f(R)理论的局部解与宇宙解.

Comprehensive analysis of relativistic embedded class-I exponential compact spheres in f(R,φ)gravity via Karmarkar condition

In this article,we use the prominent Karmarkar condition to investigate some novel features of astronomical objects in the f(R,φ)gravity;R andφrepresent the Ricci curvature and the scalar field,respectively.It is worth noting that we classify the exclusive set of modified field equations using the exponential type model of the f(R,φ)theory of gravity f(R,φ)=φ(R+α(eβR-1)).We show the embedded class-I approach via a static,spherically symmetric spacetime with an anisotropic distribution.To accomplish our objective,we use a particular interpretation of metric potential(grr)that has already been given in the literature and then presume the Karmarkar condition to derive the second metric potential.We employ distinct compact stars to determine the values of unknown parameters emerging in metric potentials.To ensure the viability and consistency of our exponential model,we execute distinct physical evolutions,i.e.the graphical structure of energy density and pressure evolution,mass function,adiabatic index,stability,equilibrium,and energy conditions.Our investigation reveals that the observed anisotropic findings are physically appropriate and have the highest level of precision.

Constraining the f(R,T)=R+2λT cosmological model using recent observational data

In this study,we conduct a comprehensive investigation of the cosmological model described by f(R,T)=R+2λT(whereλrepresents a free parameter)in light of the most recent observational data.By constraining the model using the Hubble and Pantheon datasets,we determine its compatibility with the observed behavior of the Universe.For this purpose,we adopt a parametric form for the effective equation of state(EoS)parameter.This parametric form allows us to describe the evolution of the EoS parameter with respect to redshift and investigate its behavior during different cosmic epochs.The analysis of the deceleration parameter reveals an accelerating Universe with a present value of q0=−0.64_(−0.03)^(+0.03),indicating the current phase of accelerated expansion.The transition redshift is found to be ztr=0.53_(−0.03)^(+0.04),marking the epoch of transition from deceleration to acceleration.We also analyze the evolution of important cosmological parameters,including the density parameter,pressure,effective EoS,and stability.These findings collectively demonstrate the viability of the f(R,T)cosmological model as a robust candidate capable of engendering the requisite negative pressure,thereby efficiently propelling cosmic expansion.Moreover,the undertaken stability analysis underscores the model's stability within the broader cosmic landscape.By providing the best-fit values for the coupling parameterλ,this approach motivates and encourages further exploration into the extensive landscape of this model and its potential applications across diverse realms of cosmology and astronomy.

f(T) Non-linear Massive Gravity and the Cosmic Acceleration

Inspired by the f（R） non-linear massive gravity, we propose a new kind of modified gravity model, namely f（T） non-linear massive gravity, by adding the dRGT mass term reformulated in the vierbein formalism, to the f（T） theory. We then investigate the cosmological evolution of f（T） massive gravity, and constrain it by using the latest observational data. We find that it slightly favors a crossing of the phantom divide line from the quintessence-like phase （wae 〉 -1） to the phantom-like one （wae 〈 -1） as redshiff decreases.

Charged quark stars in f(R,T)gravity

Recent advances in nuclear theory and new astrophysical observations have led to the need for specific theoretical models applicable to dense-matter physics phenomena.Quantum chromodynamics(QCD)predicts the existence of non-nucleonic degrees of freedom at high densities in neutron-star matter,such as quark matter.Within a confining quark matter model,which consists of homogeneous,neutral 3-flavor interacting quark matter with O(m_(s)^(4))corrections,we examine the structure of compact stars composed of a charged perfect fluid in the context of f(R,T)gravity.The system of differential equations describing the structure of charged compact stars has been derived and numerically solved for a gravity model with f(R,T)=R+2βT.For simplicity,we assumed that the charge density is proportional to the energy density,namely,ρ_(ch)=αρ.It is demonstrated that the matter-geometry coupling constant β and charge parameter α affect the total gravitational mass and the radius of the star.

Logarithmic Entropy Corrected Holographic Dark Energy with F(R, T ) Gravity

In this paper, we consider F(R,T) gravity as a linear function of the curvature and torsion scalars and interact it with logarithmic entropy corrected holographic dark energy to evaluate cosmology solutions. The model is investigated by FRW metric, and then the energy density and the pressure of dark energy are calculated. Also we obtain equation of state(EoS) parameter of dark energy and plot it with respect to both variable of redshift and e-folding number. Finally, we describe the scenario in three status: early, late and future time by e-folding number.

Viscosity Effects on Anisotropic Universe in Curvature-Matter Coupling Gravity

In this paper, we study evolution of the universe in the background of f(R, T) gravity using LRS Bianchi type-Ⅰ model. We discuss scale factors as well as deceleration parameter in dark energy dominated era for different bulk viscosity models. The occurrence of big-rip singularity is also examined. It is concluded that expansion is faster when bulk viscosity is proportional to Hubble parameter as compared to other models.

Effect of arbitrary matter-geometry coupling on thermodynamics in f(R)theories of gravity

In this paper,the thermodynamics of the Friedmann–Lemait re–Robertson–Walker universe have been explored in f(R)theories of gravity with arbitrary matter-geometry coupling.The equivalence between the modified Friedmann equations with any spatial curvature and the first law of thermodynamics is confirmed,where the assumption of the entropy plays a crucial role.Then laws of thermodynamics in our considering case are obtained.They can reduce to the ones given in Einstein's general theory of relativity under certain conditions.Moreover,a particular model is investigated through the obtained generalized second law of thermodynamics with observational results of cosmographic parameters.

Plane Symmetric Solutions in f(R,T) Gravity

The main purpose of this paper is to investigate the exact solutions of plane symmetric spacetime in the context of f(R,T)gravity[Phys.Rev.D 84(2011)024020],where f(R,T)is an arbitrary function of Ricci scalar R and trace of the energy momentum tensor T.We explore the exact solutions for two different classes of f(R,T)models.The first class f(R,T)=R+2f(T)yields a solution which corresponds to Taub's metric while the second class f(R,T)=f_1(R)+f_2(T)provides two additional solutions which include the well known anti-deSitter spacetime.The energy densities and corresponding functions for f(R,T)models are evaluated in each case.

Swampland dS conjecture in mimetic f(R,T)gravity

In this paper,we study a theory of gravity called mimetic f(R,T)in the presence of swampland dS conjecture.For this purpose,we introduce several inflation solutions of the Hubble parameter H(N)from f(R,T)=R+δT gravity model,in which R is Ricci scalar,and T denotes the trace of the energy–momentum tensor.Also,δand N are the free parameter and a number of e-fold,respectively.Then we calculate quantities such as potential,Lagrange multiplier,slow-roll,and some cosmological parameters such as nsand r.Then we challenge the mentioned inflationary model from the swampland dS conjecture.We discuss the stability of the model and investigate the compatibility or incompatibility of this inflationary scenario with the latest Planck observable data.

A view of compact configurations from the R+γe^xT scenario

This paper presents a picture of compact structures for the f(R,T)model of the form R+γe^χT,withγandχbeing parameters.The poly tropic equation of state and the MIT bag model reflect the pressure density relation for these compact objects.For this purpose,a system of two differential equations involving pressure as well as the mass of the stellar structure is obtained from field equations and the Tolman-Oppenheimer-Volkoff(TOV)equation.The numerical solution of this system gives a graphical description of various characteristics of these compact systems.To examine the viability and stability of assumed configurations,the energy conditions,causality relation and adiabatic index are discussed for the presumed scenario.