Statefinder Diagnostic for Born-Infeld Type Dark Energy Model

TL;DR

This paper applies the statefinder diagnostic to a Born-Infeld type dark energy model with Mexican hat potential, revealing its unique evolutionary trajectory and how it reduces to known models under certain conditions.

Contribution

It introduces the use of the statefinder diagnostic to analyze the Born-Infeld dark energy model with Mexican hat potential, highlighting its distinct evolutionary behavior.

Findings

The model's trajectory in the r(s) diagram is unique compared to other dark energy models.

The model reduces to Quintessence or ΛCDM models when kinetic energy parameters approach zero.

The statefinder diagnostic effectively distinguishes this dark energy model from others.

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.