Particle vs. future event horizon in interacting holographic dark energy model

By choosing the future event horizon as the horizon of the flat FLRW universe, we show that although the interacting holographic dark energy model is able to explain the phantom divide line crossing, but the thermodynamics second law is not respected in this model. We show that if one takes the particle event horizon as the horizon of the universe, besides describing w=-1 crossing in a consistent way with thermodynamics second law, he is able to alleviate the coincidence problem. By this choice, the first and second coincidence problems may be solved in a same framework. In this approach, after the first transition from quintessence to phantom, there is another transition from phantom to quintessence phase which avoids the big rip singularit