Reconstructing the potentials for the quintessence and tachyon dark energy, from the holographic principle

We propose an holographic quintessence and tachyon models of dark energy. The correspondence between the quintessence and tachyon energy densities with the holographic density, allows the reconstruction of the potentials and the dynamics for the quintessence and tachyon fields, in flat FRW background. The proposed infrared cut-off for the holographic energy density works for two cases of the constant $\alpha$: for $\alpha <1$ we reconstructed the holographic quintessence model in the region before the $\omega =-1$ crossing for the EoS parameter. The cosmological dynamics for $\alpha >1$ was also reconstructed for the holographic quintessence and tachyon models.