Reconstructing the f(R) gravity from the holographic principle

An holographic f® gravity model of dark energy is proposed. The correspondence between the f® geometrical effective energy density with the holographic density, allows the reconstruction of the f® gravity in flat FRW background in the Einstein frame. The proposed infrared cut-off for the holographic energy density depends on two parameters which are fit using the luminosity versus redshift data, allowing a suitable reconstruction in two representative cases of the EoS parameter: for $\omega >-1$ and $\omega <-1$.