On Two IHolgraphic Dark Energy Models

In this master's thesis, we discuss two dark energy models based on the high dimensional holographic dark energy and brane world theory.Firstly, we propose a holographic dark energy model in the DGP brane world. In this model, we modify the ultraviolet cutoff of the holographic dark energy with the 5-dimensional Schwarzschild black hole. It is found that the model will reduce to the original DGP model in the case that one of parameters equals to zero; when the another equals to zero, the model degenerates to the model that was proposed by Gong and Li. And we also find that the model was equivalent to adjust the crossover scale in standard DGP model when the infrared scale was taken as the hubble horizon scale. We find the effective equation of state may become less than -1/3 in selfaccelerating branch when the infrared cutoff was taken as the future event horizon, and in both of selfaccelerating and unselfaccelerating branches, the effective dark energy may drive the universe into accelerating phase. This is different with standard DGP model which can only speed up the selfaccelerating branch. We further let one of parameters equals to zero and take different values of the another. It is found that when effective equation of state may become less than -1. This means that the universe will suffer from a big rip singularity in the future.Secondly, we consider a high dimensional holographic dark energy model in which the matter couples to dark energy. In this model, we modified ultraviolet cutoff with 5-dimensional black hole too. Besides, we assume that the coupling term has a direct proportion relationship with the total energy density. We solve effective equation of state , relative density numerically and find that when the hubble horizon was taken as the infrared cutoff, the coupling term is zero or positive. The universe will be driven into accelerating phase in the late time and effective equation of state weff can not become less than -1. This means the universe will not suffer from big rip during the whole evolution. When the infrared cutoff is taken as the future even horizon, we obtain a couple of dynamical equations. The qualitative analysis on these equations indicates that the only critical point of the system is a saddle point.