Cosmological reconstruction and energy bounds in f (R, RαβRαβ, φ) gravity

We discuss the cosmological reconstruction of f (R, R-alpha beta R-alpha beta, phi) (where R, R-alpha beta R-alpha beta, and phi) 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 FRWuniverse 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, phi) 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.