Holographic Dark Energy Model with Hubble Horizon as an IR Cut-off

The main task of this paper is to realize a cosmic observational compatible universe in the framework of holographic dark energy model when the Hubble horizon $H$ is taken as the role of an IR cut-off. When the model parameter $c$ of a time variable cosmological constant (CC) $\Lambda(t)=3c^{2}H^{2}(t)$ becomes time or scale dependent, an extra term enters in the effective equation of sate (EoS) of the vacuum energy $w^{eff}_{\Lambda}=-c^2-d\ln c^{2}/3d\ln a$. This extra term can make the effective EoS of time variable CC cross the cosmological boundary and be phantom-like at present. For the lack of a first principle and fundamental physics theory to obtain the form $c^2$, we give a simple parameterized form of $c^2$ as an example. Then the model is confronted by the cosmic observations including SN Ia, BAO and CMB shift parameter $R$. The result shows that the model is consistent with cosmic observations.