Geometrical Diagnostic And Phase-space Analysis Of Dark Energy Models

In the last decade a convergence of independent cosmological observations suggested that the Universe is experiencing accelerated expansion. An unknown energy component, dubbed as dark energy, is proposed to explain this acceleration. Dark energy almost equally distributes in the Universe, and its pressure is negative. By far, many dark energy model have been presented .Since more and more dark energy models have been constructed, the problem of discriminating between various dark energy models is important. In this Letter, we applied two geometrical diagnostics of dark energy, involving the statefinder { , and , to distinguish purely kinetic k-essence with Dirac-Born-Infeld-like Lagrangian from LCDM model. We plotted the evolution trajectories in statefinder sr}omsr plane. We found that the statefinder cannot differentiate purely kinetic k-essence model from LCDM model at 68.3% confidence level for z ?? 1. As another diagnostic method, is widely used to distinguish different dark energy models. We found, however, the also cannot discriminate purely kinetic k-essence model and LCDM model at 68.3% confidence level.We perform a detailed phase-space analysis of a class of k-essence cosmology. We find the critical points can be divided into three classes: points unstable but the model stable, both points and the model stable, points stable but the model unstable. Like the case of points unstable but the model stable, the case of points stable but the model unstable is not relevant from a cosmological point of view, though they can be late-time attractors for the universe. So in order to study the possible final state of the universe, it is important to investigate not only the stability of the critical points but also the stability of the model. The case of both points and the model stable can further be divided into two classes: points only presenting decelerating phases and points at which all decelerating, constant-speed, and accelerating phases can appear; the final state of the universe dependents on the potential.