Statefinder Diagnostic for Born--Infeld Type Dark Energy Model

Using a new method called the statefinder diagnostics which can make one dark energy model differ from the others, we investigate the dynamics of Born--Infeld (B-I) type dark energy model. The evolution 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 η→0 or kinetic energy φ²→0, the B-I type dark energy (K-essence) model reduces to the quintessence model or the ΛCDM model corresponding to the statefinder pair r, s=1,0 respectively. As a result, the evolution trajectory of our model in the r(s) diagram in Mexican hat potential is quite different from those of other dark energy models. The current values of parameters Ω_φ and ω_φ in this model meet the latest observations WMAP5 well.