Revisit of the Interaction between Holographic Dark Energy and Dark Matter

In this paper we investigate the possible direct, non-gravitational interaction between holographic dark energy (HDE) and dark matter. Firstly, we start with two simple models with the interaction terms $Q \propto \rho_{dm}$ and $Q \propto \rho_{de}$, and then we move on to the general form $Q \propto \rho_m^\alpha\rho_{de}^\beta$. The cosmological constraints of the models are obtained from the joint analysis of the present Union2.1+BAO+CMB+$H_0$ data. We find that the data slightly favor an energy flow from dark matter to dark energy, although the original HDE model still lies in the 95.4% confidence level (CL) region. For all models we find $c<1$ at the 95.4% CL. We show that compared with the cosmic expansion, the effect of interaction on the evolution of $\rho_{dm}$ and $\rho_{de}$ is smaller, and the relative increment (decrement) amount of the energy in the dark matter component is constrained to be less than 9% (15%) at the 95.4% CL. By introducing the interaction, we find that even when $c<1$ the big rip still can be avoided due to the existence of a de Sitter solution at $z\rightarrow-1$. We show that this solution can not be accomplished in the two simple models, while for the general model such a solution can be achieved with a large $\beta$, and the big rip may be avoided at the 95.4% CL.