Holographic reconstruction of the k-essence and dilaton models

We propose an holographic $k$-essence and dilaton models of dark energy. The correspondence between the $k$-essence and dilaton energy densities with the holographic density, allows the reconstruction of the potential and the fields for the $k$-essence and dilaton models in flat FRW background. For the proposed infrared cut-off the reconstruction was made for the two cases of the constant $\alpha$: for $\alpha<1$ the model presents phantom crossing and the reconstruction was made in the region before the $\omega=-1$ crossing for the EoS parameter. The cosmological dynamics for $\alpha>1$ was also reconstructed. The reconstruction is consistent with the observational data.