Phase-space Analysis Of K-essence Dark Energy Model

With the observation of Ia supernova in1998, and the accurate data from WMAPsatellite in2003, we are shown that, the Universe is experiencing an accelerating expansion.Under the cosmologic principle and general relativity, to explain this phenomenal, we mustintroduce a new material, that is the dark energy. The cosmological constant (the vacuumenergy) is the simplest candidate, but it has the cosmological constant problem and ageproblem.To solve the two problems above, physicists come up with many dynamical dark energymodels. Among them, the k-essence model will be chosen in our thesis. We consider twocases: first, there is no interaction between the dark matter and the dark energy; second, thereare some certain interactions Q H m, between the dark matter and the dark energy. Thepower-law form k-essence modelF (X) X Xwas studied. After solving theself-contain dynamical equation, many critical points are obtained. The first step,settingQ0, that is to say there is no interaction between the dark matter and the dark energy,eight critical points are obtained. Then in the second step, choosing Q H m, that is to saythere are some certain interactions between the dark matter and the dark energy, six criticalpoints were obtained. The existence and the stability condition for all fourteen critical pointsare discussed respectively. Meanwhile, the stability of the models are discussed, including theclassical stability and quantum stability. Upon the above research, also we calculated thecosmologic parameters, and get the range of parameters for the accelerating expansion. Wefound that in our model, the dark energy equation could over-1, which provide the theoreticalevidence for future observation.