Anisotropic quark stars in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

The aim of this paper is to analyze the nature of anisotropic spherically symmetric relativistic star models in the framework of f(R, T) gravity. To discuss the features of compact stars, we consider that in the interior of the stellar system, the fluid distribution is influenced by MIT bag model equation of state. We construct the field equations by employing Krori–Barua solutions and obtain the values of unknown constants with the help of observational data of Her X-1, SAX J 1808.4-3658, RXJ 1856-37 and 4U1820-30 star models. For a viable f(R, T) model, we study the behavior of energy density, transverse as well as radial pressure and anisotropic factor in the interior of these stars for a specific value of the bag constant. We check the physical viability of our proposed model and stability of stellar structure through energy conditions, causality condition and adiabatic index. It is concluded that our model satisfies the stability criteria as well as other physical requirements, and the value of bag constant is in well agreement with the experimental value which highlights the viability of our considered model.     

Cosmology in modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>)-gravity

In the present paper we propose a further modification of f(R, T)-gravity (where T is trace of the energy-momentum tensor) by introducing higher derivatives matter fields. We discuss stability conditions in the proposed theory and find restrictions for the parameters to prevent appearance of main type of instabilities, such as ghost-like and tachyon-like instabilities. We derive cosmological equations for a few representations of the theory and discuss main differences with conventional f(R, T)-gravity without higher derivatives. It is demonstrated that in the theory presented inflationary scenarios appear quite naturally even in the dust-filled Universe without any additional matter sources. Finally, we construct an inflationary model in one of the simplest representation of the theory, calculate the main inflationary parameters and find that it may be in quite good agreement with observations.     

Exact solutions and conserved quantities in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper explores Noether and Noether gauge symmetries of anisotropic universe model in f(R, T) gravity. We consider two particular models of this gravity and evaluate their symmetry generators as well as associated conserved quantities. We also find exact solution by using cyclic variable and investigate its behavior via cosmological parameters. The behavior of cosmological parameters turns out to be consistent with recent observations which indicates accelerated expansion of the universe. Next we study Noether gauge symmetry and corresponding conserved quantities for both isotropic and anisotropic universe models. We conclude that symmetry generators and the associated conserved quantities appear in all cases.     

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.     

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.     

The anisotropic cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity with <Emphasis Type="Italic">Λ(T)</Emphasis>

The rare decay \(B\rightarrow {K^{*}}\ell ^+\ell ^-\) is a very significant mode to search for physics beyond the Standard Model (SM). The mode provides a very rich spectrum of observables obtained from the angular distribution of its decay products. The recent LHCb measured values of these observables are used to conclude an evidence of right-handed currents at the kinematic endpoint of this decay mode. As the conclusion is drawn at the maximum dilepton invariant mass square (\(q^2\)) kinematic endpoint, it relies only on heavy quark symmetries where it is valid without significant corrections.     

Effects of charge on dynamical instability of spherical collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

The effects of charge on stable structure of spherically symmetric collapsing model comprising anisotropic matter distribution are studied in f(R, T) gravity, where R and T correspond to scalar curvature and trace of the energy-momentum tensor, respectively. We construct the field equations, Maxwell equations and dynamical equations in this scenario. We employ linear perturbation scheme on physical variables, metric functions as well as modified terms to establish the evolution or collapse equation for a consistent functional form of f(R, T) gravity. We investigate the limit of instability in Newtonian as well as post Newtonian regimes. It is found that charge plays a fundamental role to slow down the collapse and form a more stable system.     

Palatini formulation of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity theory,and its cosmological implications

We consider the Palatini formulation of f(R, T) gravity theory, in which a non-minimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similar to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the f(R, T) gravity in the Palatini formulation. Cosmological models with Lagrangians of the type \(f=R-\alpha ^2/R+g(T)\) and \(f=R+\alpha ^2R^2+g(T)\) are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.     

Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity models with curvature–matter coupling

A modified f(G) gravity model with coupling between matter and geometry is proposed, which is described by the product of the Lagrange density of the matter and an arbitrary function of the Gauss–Bonnet term. The field equations and the equations of motion corresponding to this model show the non-conservation of the energy-momentum tensor, the presence of an extra force acting on test particles and non-geodesic motion. Moreover, the energy conditions and the stability criterion at the de Sitter point in modified f(G) gravity models with curvature–matter coupling are derived, which can degenerate to the well-known energy conditions in general relativity. Furthermore, in order to get some insight in the meaning of these energy conditions, we apply them to the specific models of f(G) gravity and the corresponding constraints on the models are given. In addition, the conditions and the candidate for late-time cosmic accelerated expansion in modified f(G) gravity are studied by means of conditions of power-law expansion and the equation of state of matter ω smaller than -\frac13-\frac{1}{3}.     

Extended Birkhoff’s theorem in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, Eur. Phys. J. (2011), ], we prove that Birkhoff’s theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss, respectively, the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of Birkhoff’s theorem in the frame of f(T) gravity via a conformal transformation by regarding the Brans–Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.     

Birkhoff’s theorem in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

Generalized from the so-called teleparallel gravity, which is exactly equivalent to general relativity, f(T) gravity has been proposed as an alternative gravity model to account for the dark energy phenomena. In this letter we prove that the external vacuum gravitational field for a spherically symmetric distribution of source matter in the f(T) gravity framework must be static. The conclusion is independent of the radial distribution and spherically symmetric motion of the source matter, that is, whether it is in motion or static. As a consequence, the Birkhoff’s theorem is valid in the general nonsingular f(T) theory at the un-perturbative level. We also discuss its application in the de Sitter spacetime evolution phase as preferred by present dark energy observations.     

Plane Symmetric Vacuum Bianchi Type <Emphasis Type="Italic">III</Emphasis> Cosmology in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Gravity

The main purpose of this paper is to study the exact solution of Bianchi type III spacetime in the context of metric f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives C=A ⁿ , where A and C are the metric coefficients. The physical behavior of the solution has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.     

On the <Emphasis Type="Italic">Λ</Emphasis>CDM Universe in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

In the context of the so-called Gauss–Bonnet gravity, where the gravitational action includes function of the Gauss–Bonnet invariant, we study cosmological solutions, especially the well-known ΛCDM model. It is shown that the dark energy contribution and even the inflationary epoch can be explained in the frame of this kind of theories with no need of any other kind of component. Other cosmological solutions are constructed and the rich properties that this kind of theories provide are explored.     

A dynamical system approach to Bianchi III cosmology for Hu–Sawicki type <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The cosmological dynamics of spatially homogeneous but anisotropic Bianchi type-III space-time is investigated in presence of a perfect fluid within the framework of Hu–Sawicki model. We use the dynamical system approach to perform a detailed analysis of the cosmological behaviour of this model for the model parameters \(n=1, c_1=1\), determining all the fixed points, their stability and corresponding cosmological evolution. We have found stable fixed points with de Sitter solution along with unstable radiation like fixed points. We have identified a matter like point which act like an unstable spiral and when the initial conditions of a trajectory are very close to this point, it stabilizes at a stable accelerating point. Thus, in this model, the universe can naturally approach to a phase of accelerated expansion following a radiation or a matter dominated phase. It is also found that the isotropisation of this model is affected by the spatial curvature and that all the isotropic fixed points are found to be spatially flat.     

Early and late-time cosmic acceleration in non-minimal Yang–Mills-<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

In this paper we show that power-law inflation can be realized in non-minimal gravitational coupling of Yang–Mills field with a general function of the Gauss–Bonnet invariant in the framework of Einstein gravity. Such a non-minimal coupling may appear due to quantum corrections. We also discuss the non-minimal Yang–Mills-f(G) gravity in the framework of modified Gauss–Bonnet action which is widely studied recently. It is shown that both inflation and late-time cosmic acceleration are possible in such a theory.     

Revised Spherically Symmetric Solutions of <Emphasis Type="Italic">R</Emphasis>+<Emphasis Type="Italic">ε</Emphasis>/<Emphasis Type="Italic">R</Emphasis> Gravity

We study spherically symmetric static empty space solutions in R+ε/R model of f(R) gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general solutions which are perturbed Schwarzschild metric and viable for solar system. Our results for large scale contains a logarithmic term with a coefficient producing a repulsive gravity force which is in agreement with the positive acceleration of the universe.     

On a Ströbel-Inspired <Emphasis Type="Italic">k</Emphasis>(<Emphasis Type="Italic">t</Emphasis>) FLRW Ansatz in a Class of Metric <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Models

Assuming a D≥4 dimensional FLRW (Friedmann–Lemaître–Robertson–Walker) inspired ansatz with spatial curvature being a non-trivial function of time k(t) in a class of metric and Jordan frame F(R) gravity models, non-existence theorems for several types of sources are derived in a simple manner (using specific form of the modified gravity Einstein tensor components).