Scalar Field Reconstructions of Standard, Power Law and Logarithmic Holographic Dark Energy with a Gauss-Bonnet IR cut-off

In this paper, we investigate the Holographic Dark Energy (HDE) model and its entropy-corrected versions, namely the Power Law and Logarithmic entropy corrected HDE models, by considering the infrared cut-off $L={\mathcal{G}}^{-1\mathrm{/}4}$, where $\mathcal{G}$ is the Gauss-Bonnet invariant. We derived the Equation of State parameter ${\omega }_D$, the deceleration parameter $q$ and the evolutionary form of the fractional energy density of DE ${\mathrm{\Omega }}_D^{\mathrm{\prime }}$ for flat and non-flat universes, with and without interaction between DE and Dark Matter. We also analyzed the asymptotic behavior in the DE dominated epoch. Furthermore, correspondences between the considered HDE models and several scalar field models, including tachyon, k-essence, quintessence, Generalized Chaplygin Gas, Yang-Mills, and Nonlinear Electrodynamics models, were established.