Several parametrization dark energy models comparison with Statefinder hierarchy

TL;DR

This study compares various parametrized dark energy models using the Statefinder hierarchy and growth rate of matter perturbations, finding specific derivatives that effectively distinguish models from the standard b1CDM cosmology.

Contribution

It demonstrates the effectiveness of higher-order Statefinder parameters in differentiating dark energy models from b1CDM, highlighting the limited role of matter perturbation growth rate.

Findings

Statefinder $S_3^{(m)}$ distinguishes CPL and JBP from b1CDM and Pade9 models.

Statefinder $S_4^{(1)}$ more effectively distinguishes Pade9 models from b1CDM.

Growth rate of matter perturbations has limited discriminative power.

Abstract

We employ the Statefinder hierarchy and the growth rate of matter perturbations to explore the discrimination of $\Lambda$CDM and some parametrization dark energy models including the Chevallier-Polarski-Linder (CPL), the Jassal-Bagla-Padmanabhan (JBP), the Pad\'{e}(\uppercase\expandafter{\romannumeral1}), (\uppercase\expandafter{\romannumeral2}). We find that the statefinder $S_3^{(m)}$ containing third derivatives of $a(t)$ can differentiate CPL and JBP from $\Lambda$CDM and Pad\'{e}(\uppercase\expandafter{\romannumeral1}), (\uppercase\expandafter{\romannumeral2}). While the statefinder $S_4^{(1)}$ involving fourth order derivatives of $a(t)$ has more powerful discrimination that it can distinguish the Pad\'{e}(\uppercase\expandafter{\romannumeral1}), (\uppercase\expandafter{\romannumeral2}) from $\Lambda$CDM. In addition, we show that the growth rate of matter perturbations does not play a significant role for discrimination of such parametrization dark energy models.