Universe Dynamics Study Of A Number Of Issues

In this master dissertation, under the fundamental frame of general relativity, we study the dynamics of two types of dark energy models—quintessence, phantom and DGP brane model by using phase space method.Firstly, we briefly look back the history of cosmology and picture the standard hot big bang model.Then, in order to make a theoretical preparation, we describe the origin of dark energy and brane world, especially we discuss the quintessence and phantom and DGP models respectively.After above review, we study the dynamics of phantom model with multi-exponential potential which has N scalar fields. We show that big rip attractors would exist in the case of N = 2 phantom models with a given potential.At last, we consider a quintessence model with single or double exponential potential under the framework of DGP model. Using the method of dynamical analysis technique, we show that there are different cosmic late-time behavior. And the stability also brings some constraints on the potential.