Holographic dark energy in Brans-Dicke theory with log correction

Abstract: In the derivation of holographic dark energy density, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity, string theory and black hole physics. In this paper, we study cosmological implication of the interacting entropy-corrected holographic dark energy model in the framework of Brans-Dicke cosmology. We obtain the equation of state and the deceleration parameters of the entropy-corrected holographic dark energy in a non-flat Universe. As system's IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as $L=ar(t)$. We find out that when the entropy-corrected holographic dark energy is combined with the Brans-Dicke field, the transition from normal state where $w_D >-1 $ to the phantom regime where $w_D <-1 $ for the equation of state of interacting dark energy can be more easily achieved for than when resort to the Einstein field equations is made.