We discuss the cosmological reconstruction of f (R, R αβ R αβ , φ) (where R, R αβ R αβ , and φ represent the Ricci scalar, the Ricci invariant, and the scalar field) corresponding to a power law and de Sitter evolution in the framework of the FRW universe model. We derive the energy conditions for this modified theory which seem to be more general and can be reduced to some well-known forms of these conditions in general relativity, f (R) and f (R, φ) theories. We have presented the general constraints in terms of recent values of the snap, jerk, deceleration, and Hubble parameters. The energy bounds are analyzed for reconstructed as well as known models in this theory. Finally, the free parameters are analyzed comprehensively.

No abstract

In this paper, we examine static spherically symmetric wormhole solutions in generalized f (R, φ) gravity. To do this, we consider three different kinds of fluids: anisotropic, barotropic and isotropic. We explore different f (R, φ) models and inspect the energy conditions for all of those three fluids. It is found that under some models in this theory, it is possible to obtain wormhole solutions without requiring exotic matter. The discussion about the conditions where the standard energy conditions (WEC and NEC) are valid for the fluids is discussed in details. From our results and for our cases, we conclude that for anisotropic and isotropic fluids, realistic wormhole geometries satisfying the energy conditions can be constructed.

No abstract

First and second laws of black hole thermodynamics are examined at the apparent horizon of FRW spacetime in f (R, R αβ R αβ , φ) gravity, where R, R αβ R αβ and φ are the Ricci scalar, Ricci invariant and the scalar field respectively. In this modified theory, Friedmann equations are formulated for any spatial curvature. These equations can be presented into the form of first law of thermodynamics for T h d Ŝh + T h d i Ŝh + W dV = dE, where d i Ŝh is an extra entropy term because of the non-equilibrium presentation of the equations and T h d Ŝh +W dV = dE for the equilibrium presentation. The generalized second law of thermodynamics (GSLT) is expressed in an inclusive form where these results can be represented in GR f (R) and f (R, φ) gravities. Finally to check the validity of GSLT, we take some particular models and produce constraints of the parameters.