| With the discovery of the present cosmic acceleration in1998. dark Energy has been one of the most important issues in the Research of cosmology. In this thesis, beginning with the discussion on the cosmological dynamics and the cosmic acceleration,Then several dynamical dark energy models are reviewed in chapter2. In chapter3,we discuss the inconsistences in interacting Agegraphic dark energy model. we recall the inconsistence in the origin agegraphic dark energy model that the agegraphic dark energy tracks the matter in the matter-dominated epoch. And furthermore, we point out that there is the other more serious inconsistence in the model that the matter-dominated epoch contradicts the ability of agegraphic dark energy in driving the accelerated expansion. By considering three kinds of phenomenological interaction between the agegraphic dark energy and matter, we analyze the interacting agegraphic dark energy models. we find that the existence of the matter-dominated epoch contradicts the ability of agegraphic dark energy in driving the accelerated expansion even in the interacting models.If our universe is going through a phase of accelerated expansion at present time, Then it is interesting to study the problem of the dark energy accretion on black holes in an expanding universe. By using a solution describing a black hole imbedded in a FLRW universe and chosing imperfect fluid with no radial mass flow as distribution of cosmic matter, we get a evolving equation of black hole expressed in terms of cosmological parameters in chapter4. The evolving equation of black hole allows the increase of black hole due to the accretion of phantom energy. We can see different model of the matter distribution in universe may lead to different fate of black hole due to the accretion of phantom energy. |