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f(R) in Holographic and Agegraphic Dark Energy Models and the Generalized Uncertainty Principle

We studied a unified approach with the holographic, new agegraphic and the $f(R)$ dark energy model to construct the form of $f(R)$ which in general responsible for the curvature driven explanation of the very early inflation along with presently observed late time acceleration. We considered the generalized uncertainty principle in our approach which incorporated the corrections in the entropy area relation and thereby modified the energy densities for the cosmological dark energy models considered. We found that holographic and new agegraphic $f(R)$ gravity models can behave like phantom or quintessence models in the spatially flat FRW universe. We also found a distinct term in the form of $f(R)$ which goes as $R^{\frac{3}{2}}$ due to the consideration of the GUP modified energy densities. Although the presence of this term in the action can have its importance in explaining the early inflationary scenario but Capozziello {\it et.al.} recently showed that $f(R) \sim R^{\frac{3}{2}}$ leads to an accelerated expansion, {\it i.e.}, a negative value for the deceleration parameter $q$ which fit well with SNeIa and WMAP data.