Diagnosing holographic dark energy models with statefinder hierarchy

TL;DR

This paper uses statefinder hierarchy diagnostics combined with growth parameters to distinguish between various holographic dark energy models, finding that certain diagnostics are more effective and can break model degeneracies.

Contribution

It introduces a combined diagnostic approach using statefinder hierarchy and growth parameters to effectively differentiate holographic dark energy models.

Findings

$S^{(1)}_4$ outperforms $S^{(1)}_3$ in model diagnosis.

The combined method helps break degeneracies in the new agegraphic dark energy model.

Statefinder hierarchy and growth parameters together provide a powerful diagnostic tool.

Abstract

We apply a series of null diagnostics based on the statefinder hierarchy to diagnose different holographic dark energy models including the original holographic dark energy, the new holographic dark energy, the new agegraphic dark energy, and the Ricci dark energy models. We plot the curves of statefinders $S^{(1)}_3$ and $S^{(1)}_4$ versus redshift $z$ and the evolutionary trajectories of $\{S^{(1)}_3, \epsilon\}$ and $\{S^{(1)}_4, \epsilon\}$ for these models, where $\epsilon$ is the fractional growth parameter. Combining the evolution curves with the current values of $S^{(1)}_3$, $S^{(1)}_4$, and $\epsilon$, we find that the statefinder $S^{(1)}_4$ performs better than $S^{(1)}_3$ for diagnosing the holographic dark energy models. In addition, the conjunction of the statefinder hierarchy and the fractional growth parameter is proven to be a useful method to diagnose the holographic dark energy models, especially for breaking the degeneracy of the new agegraphic dark energy model with different parameter values.