Statefinder Diagnostic for Born-Infeld Type Dark Energy Model

Abstract

Using a new method--statefinder diagnostic which can differ one dark energy model from the others, we investigate in this letter the dynamics of Born-Infeld(B-I) type dark energy model. The evolutive trajectory of B-I type dark energy with Mexican hat potential model with respect to $e-folding$ time $N$ is shown in the $r(s)$ diagram. When the parameter of noncanonical kinetic energy term $\eta\to0$ or kinetic energy $\dot{\phi}^2\to0$, B-I type dark energy(K-essence) model reduces to Quintessence model or $\Lambda$CDM model corresponding to the statefinder pair $\{r, s\}$=$\{1, 0\}$ respectively. As a result, the the evolutive trajectory of our model in the $r(s)$ diagram in Mexican hat potential is quite different from those of other dark energy models.