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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, Ricciinvariant and scalar field) corresponding to power law and de Sitter evolutionin the framework of FRW universe model. We derive the energy conditions forthis modified theory which seem to be more general and can be reduced to someknown forms of these conditions in general relativity, $f(R)$ and $f(R,\phi)$theories. We have presented the general constraints in terms of recent valuesof snap, jerk, deceleration and Hubble parameters. The energy bounds areanalyzed for reconstructed as well as known models in this theory. Finally, thefree parameters are analyzed comprehensively.

Cosmological reconstruction and energy bounds in $f(R,R_{\alpha \beta}R^{\alpha\beta},\phi)$ gravity