Holographic Dark Energy in Brans-Dicke Theory

In this paper, the holographic dark energy model is considered in Brans-Dicke theory where the holographic dark energy density $\rho_{\Lambda} =3c^2 M^{2}_{pl} L^{-2}$ is replaced with $\rho_{h}=3c^2 \Phi(t)L^{-2}$. Here $\Phi(t)=\frac{1}{8\pi G}$ is a time variable Newton constant. With this replacement, it is found that no accelerated expansion universe will be achieved when the Hubble horizon is taken as the role of IR cut-off. When the event horizon is adopted as the IR cut-off, an accelerated expansion universe is obtained. In this case, the equation of state of holographic dark energy $w_h$ takes a modified form $w_h=-{1/3}(1+\alpha+\frac{2}{c}\sqrt{\Omega_{h}})$. In the limit $\alpha\to 0$, the 'standard' holographic dark energy is recovered. In the holographic dark energy dominated epoch, power-law and de Sitter time-space solutions are obtained.