Discriminating dark energy models by using the statefinder hierarchy and the growth rate of matter perturbations

TL;DR

This paper uses the statefinder hierarchy and growth rate of matter perturbations to effectively distinguish between various dark energy models, including Chaplygin gas variants, k-essence, and the standard b3CDM, at the present epoch.

Contribution

It introduces a composite diagnostic approach that successfully discriminates multiple dark energy models using the statefinder hierarchy and growth rate data.

Findings

The composite diagnostic (z), S^{(1)}_{5} effectively distinguishes all considered models.

Other diagnostic combinations are less effective, with some models remaining indistinguishable.

The methods provide a clear way to differentiate dark energy models at the current epoch.

Abstract

We apply the Statefinder hierarchy and the growth rate of matter perturbations to discriminate modified Chaplygin gas (MCG), generalized Chaplygin gas (GCG), superfluid Chaplygin gas (SCG), purely kinetic k-essence (PKK), and $\Lambda$CDM model. We plot the evolutional trajectories of these models in the statefinder plane and in the composite diagnostic plane. We find that GCG, MCG, SCG, PKK, and $\Lambda$CDM can be distinguished well from each other at the present epoch by using the composite diagnostic $\{\epsilon(z), S^{(1)}_{5}\}$. Using other combinations, such as $\{S^{(1)}_{3}, S^{(1)}_4\}$, $\{S^{(1)}_{3}, S_{5}\}$, $\{\epsilon(z), S^{(1)}_{3}\}$, and $\{\epsilon(z), S_4 \}$, some of these five dark energy models cannot be distinguished.