Geometrical diagnostic for purely kinetic k-essence dark energy

Abstract: Geometrical diagnostic, involving the statefinder ${r,s}$ and $Om(x)$, is widely used to discriminate different dark energy models. We apply the statefinder ${r,s}$ and $Om(x)$ to purely kinetic k-essence dark energy model with Dirac-Born-Infeld-like Lagrangian which can be considered as scalar field realizations of Chaplygin gas. We plot the evolution trajectories of this model in the statefinder parameter-planes and $Om(x)$ parameter-plane. We find that the statefinder ${r,s}$ and $Om(x)$ fail to distinguish purely kinetic k-essence model from $\Lambda$CDM model at 68.3% confidence level for $z\ll 1$.