Geometrical diagnostic for purely kinetic k-essence dark energy

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 ΛCDM model at 68.3% confidence level for z≪1.