The holographic dark energy in non-flat Brans-Dicke cosmology

In this paper we study cosmological application of holographic dark energy density in the Brans-Dicke framework. We employ the holographic model of dark energy to obtain the equation of state for the holographic energy density in non-flat (closed) universe enclosed by the event horizon measured from the sphere of horizon named $L$. Our calculation show, taking $\Omega_{\Lambda}=0.73$ for the present time, the lower bound of $w_{\rm \Lambda}$ is -0.9. Therefore it is impossible to have $w_{\rm \Lambda}$ crossing -1. This implies that one can not generate phantom-like equation of state from a holographic dark energy model in non-flat universe in the Brans-Dicke cosmology framework. In the other hand, we suggest a correspondence between the holographic dark energy scenario in flat universe and the phantom dark energy model in framework of Brans-Dicke theory with potential.