Geometrical diagnostic for purely kinetic k-essence dark energy

TL;DR

This paper evaluates the effectiveness of geometrical diagnostics, specifically the statefinder r,s and  (x), in distinguishing purely kinetic k-essence dark energy models from the  model, finding they are ineffective at low redshift.

Contribution

It applies the statefinder and  diagnostics to a specific k-essence dark energy model and assesses their ability to differentiate it from  .

Findings

Statefinder r,s and  (x) fail to distinguish the model from  at low redshift.

Trajectories in diagnostic planes resemble  , indicating degeneracy.

Diagnostics are ineffective for  -like models at z  1.

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 $z\ll 1$.