Cosmological reconstruction and energy bounds in $f(R,R_{\alpha \beta}R^{\alpha\beta},\phi)$ 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 $\phi$ represents the Ricci scalar, Ricci invariant and scalar field) corresponding to power law and de Sitter evolution in the framework of FRW universe model. We derive the energy conditions for this modified theory which seem to be more general and can be reduced to some 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 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.