expansion of the universe only the holographic and the new agegraphic DE model is somehow based on the entropy-area relation. The entropy-area relation on the other hand can have quantum corrections through various approaches of quantum gravity.

As no single theoretical proposal for DE enjoys a pronounced supremacy over the others in terms of having a strong field theoretic support as well as being able to explain all the present observational data. This state of art explores another possibility of whether geometry in its own right could explain the presently observed accelerated expansion. The idea stems from the fact that higher order modifications of the Ricci curvature $R$ along with $R$ in the Einstein-Hilbert action could generate inflation in the very early universe. As the curvature is expected to fall off with the cosmic evolution it is then obvious whether inverse powers of $R$ in the action dominant during the later stages could drive a late time acceleration. In general this alternative theory is coined as $f(R)$ gravity.

In this paper we studied a unified approach with the holographic, new agegraphic and the $f(R)$ DE model to construct the form of $f(R)$ which in general responsible for the curvature driven 