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.     

Static spherically symmetric solutions in <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

A Lagrangian derivation of the Equations of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented. For a large class of metrics, our approach permits one to reduce the EOM to a single equation and we show how it is possible to construct exact solutions in F(R)-gravity. All known exact solutions are recovered. We also exhibit a new non-trivial solution with non-constant Ricci scalar.     

Stability analysis of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>)-AdS black holes

We study the stability of the f(R)-AdS (Schwarzschild–AdS) black hole obtained from f(R) gravity. In order to resolve the difficulty of solving fourth-order linearized equations, we transform f(R) gravity into scalar–tensor theory by introducing two auxiliary scalars. In this case, the linearized curvature scalar becomes a dynamical scalaron, showing that all linearized equations are second order. Using the positivity of gravitational potentials and S-deformed technique allows us to guarantee the stability of f(R)-AdS black hole if the scalaron mass squared satisfies the Breitenlohner–Freedman bound. This is confirmed by computing quasinormal frequencies of the scalaron for the f(R)-AdS black hole.     

Energy distribution in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity

The well-known energy problem is discussed in f (R) theory of gravity. We use the generalized Landau–Lifshitz energy–momentum complex in the framework of metric f (R) gravity to evaluate the energy density of plane symmetric solutions for some general f (R) models. In particular, this quantity is found for some popular choices of f (R) models. The constant scalar curvature condition and the stability condition for these models are also discussed. Further, we investigate the energy distribution of cosmic string spacetime.     

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.     

Spherical Symmetric Solution in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Model Around Charged Black Hole

A static, asymptotically flat, spherically symmetric solutions is investigated in f(R) theories of gravity for a charged black hole. We have studied the weak field limit of f(R) gravity for the some f(R) model such as f(R)=R+ε h(R). In particular, we consider the case lim  _R→0 h(R)/h′(R)→0 and find the space time metric for f(R)=R+[(m⁴)/(R)]f(R)=R+{\mu^{4}\over R} and f(R)=R ^1+ε theories of gravity far away a charged mass point.     

<Emphasis Type="Italic">C</Emphasis>-field Cosmological Models with Variable <Emphasis Type="Italic">G</Emphasis> in FRW Space–Time

C-field cosmological models based on Hoyle-Narlikar theory with variable gravitational constant G in the frame work of FRW (Friedmann-Robertson-Walker) space–time for positive and negative curvatures are investigated. To get the deterministic solutions in terms of cosmic time t, we have assumed G=R ⁿ and discussed for n=−1, −2, R being scalar factor. In both the cases, creation field C increases with time, the gravitational constant G and matter density (ρ) decrease with time in the model (21). In the model (41) G decreases with time and matter density (ρ) is constant. The other physical aspects of the models are also discussed.     

Graviton and scalar propagations on AdS<Subscript>4</Subscript> space in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravities

We investigate propagations of graviton and additional scalar on four-dimensional anti-de Sitter (AdS₄) space using f(R) gravity models with external sources. It is shown that there is the van Dam–Veltman–Zakharov (vDVZ) discontinuity in f(R) gravity models because f(R) gravity implies GR with additional scalar. This clearly indicates a difference between general relativity and f(R) gravity.     

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.     

Charmless nonleptonic <Emphasis Type="Italic">B</Emphasis> decays into scalar and pseudoscalar mesons

The charmless nonleptonic decay modes B → f ₀ K(π) involving a scalar and a pseudoscalar meson in the final state are studied. The scalar meson f ₀ is considered as a q̄q state, as favored by some recent studies. Using the generalized factorization approach, the branching ratios and CP violation parameters are computed for these modes. The form factors are calculated using the results from relativistic light front quark model and the ISGW2 model. It is found that the direct CP violation parameters in these modes are small. However, the obtained branching ratios are not in agreement with the experimental data. Therefore, these modes may be considered as possible probes for new physics.      

Hawking radiation of black holes in non-minimal <Emphasis Type="Italic">R</Emphasis><Superscript><Emphasis Type="Italic">β</Emphasis></Superscript><Emphasis Type="Italic">F</Emphasis><Superscript>2</Superscript>-type coupled Einstein–Maxwell theory

We investigate the Hawking radiation and greybody factor for a scalar field on the background of the black holes in the theory of the non-minimal R ^β F ²-coupled electromagnetic fields to gravity. For different asymptotic structures caused by the real power number β, we find that the influences of the real power number on the Hawking radiation and greybody factor are different. We also show that the different coupling constant also affects the Hawking radiation and greybody factor.     

<Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity constrained by PPN parameters and stochastic background of gravitational waves

We analyze seven different viable f (R)-gravities towards the Solar System tests and stochastic gravitational waves background. The aim is to achieve experimental bounds for the theory at local and cosmological scales in order to select models capable of addressing the accelerating cosmological expansion without cosmological constant but evading the weak field constraints. Beside large scale structure and galactic dynamics, these bounds can be considered complimentary in order to select self-consistent theories of gravity working at the infrared limit. It is demonstrated that seven viable f (R)-gravities under consideration not only satisfy the local tests, but additionally, pass the above PPN-and stochastic gravitational waves bounds for large classes of parameters.     

New types of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

Recently f(T) theories based on modifications of teleparallel gravity, where torsion is the geometric object describing gravity instead of curvature, have been proposed to explain the present cosmic accelerating expansion. The field equations are always second order, remarkably simpler than f(R) theories. In analogy to the f(R) theory, we consider here three types of f(T) gravity, and find that all of them can give rise to cosmic acceleration with interesting features, respectively.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity solutions for evolving wormholes

The scalar–tensor f(R) theory of gravity is considered in the framework of a simple inhomogeneous space-time model. In this research we use the reconstruction technique to look for possible evolving wormhole solutions within viable f(R) gravity formalism. These f(R) models are then constrained so that they are consistent with existing experimental data. Energy conditions related to the matter threading the wormhole are analyzed graphically and are in general found to obey the null energy conditions (NEC) in regions around the throat, while in the limit \(f(R)=R,\) NEC can be violated at large in regions around the throat.     

The <Emphasis Type="Italic">Φ</Emphasis>→K<Superscript>0</Superscript>¯<Emphasis Type="Italic">γ</Emphasis> decay

The scalar contributions to the radiative decay φ→K ⁰ˉ⁰ γ are studied within the framework of the Linear Sigma Model (LσM). Theoretical predictions for the associated subprocesses φ→f ₀ γ and φ→a ₀ γ as well as the ratio φ→f ₀ γ/a ₀ γ are also given.     

Strong energy condition and the repulsive character of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The Raychaudhuri equation enables to examine the whole spacetime structure without specific solutions of Einstein’s equations, playing a central role for the understanding of the gravitational interaction in cosmology. In General Relativity, without considering a cosmological constant, a non-positive contribution in the Raychaudhuri equation is usually interpreted as the manifestation of the attractive character of gravity. In this case, particular energy conditions—indeed the strong energy condition—must be assumed in order to guarantee the attractive character. In the context of f(R) gravity, however, even assuming the standard energy conditions one may have a positive contribution to the Raychaudhuri equation. Besides providing a simple way to explain the observed cosmic acceleration, this fact opens the possibility of a repulsive character of this kind of gravity. In order to discuss physical bounds on f(R) models, we address the attractive/non-attractive character of f(R) gravity considering the Raychaudhuri equation and assuming the strong energy condition along with recent estimates of the cosmographic parameters.     

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.     

Dark-energy cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

We discuss dark-energy cosmological models in f(G) gravity. For this purpose, a locally rotationally symmetric Bianchi type I cosmological model is considered. First, exact solutions with a well-known form of the f(G) model are explored. One general solution is discussed using a power-law f(G) gravity model and physical quantities are calculated. In particular, Kasner’s universe is recovered and the corresponding f(G) gravity models are reported. Second, the energy conditions for the model under consideration are discussed using graphical analysis. It is concluded that solutions with f(G) = G^5/6 support expansion of universe while those with f(G) = G^1/2 do not favor the current expansion.     

<Emphasis Type="Italic">O</Emphasis>(1) eV sterile neutrino in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We refer [1] to the role of an additional O(1) eV sterile neutrino in modified gravity models. We find parameter constraints in particular f(R) gravity model using following up-to-dated cosmological data: measurements of the cosmic microwave background (CMB) anisotropy, the CMB lensing potential, the baryon acoustic oscillations (BAO), the cluster mass function and the Hubble constant. It was obtained for the sterile neutrino mass 0.47 eV < m _ν,sterile < 1 eV (2σ) assuming that the sterile neutrinos are thermalized and the active neutrinos are massless, not significantly larger than in the standard cosmology model within the same data set: 0.45 eV < m _ν,sterile < 0.92 eV (2σ). But, if the mass of sterile neutrino is fixed and equals ≈ 1.5 eV according to various anomalies in neutrino oscillation experiments, f(R) gravity is much more consistent with observation data than the CDM model.     

Non-vacuum Bianchi types <Emphasis Type="Italic">I</Emphasis> and <Emphasis Type="Italic">V</Emphasis> in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity

In a recent paper (Sharif and Shamir in Class. Quantum Grav. 26:235020, 2009), we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f (R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to find energy density and pressure of the universe. In particular, we find two exact solutions in each case which correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.