Statefinder hierarchy exploration of the extended Ricci dark energy

TL;DR

This paper investigates the extended Ricci dark energy model using the statefinder hierarchy and fractional growth parameter, demonstrating how various parameter combinations can distinguish ERDE from the standard $ ext{Lambda}$CDM model across different redshift regions.

Contribution

The study introduces a comprehensive analysis of ERDE using higher-order statefinders and growth parameters, revealing effective parameter combinations for model discrimination.

Findings

$S_3^{(1)}$ effectively differentiates ERDE from $ ext{Lambda}$CDM.

Combinations $ ext{S}_n^{(1)}$ and $ ext{epsilon}$ break degeneracy at high redshift.

$S_3^{(1)}$ is the best discriminator within ERDE and from $ ext{Lambda}$CDM.

Abstract

We apply the statefinder hierarchy plus the fractional growth parameter to explore the extended Ricci dark energy (ERDE) model, in which there are two independent coefficients $\alpha$ and $\beta$. By adjusting them, we plot evolution trajectories of some typical parameters, including Hubble expansion rate $E$, deceleration parameter $q$, the third and fourth order hierarchy $S_3^{(1)}$ and $S_4^{(1)}$ and fractional growth parameter $\epsilon$, respectively, as well as several combinations of them. For the case of variable $\alpha$ and constant $\beta$, in the low-redshift region the evolution trajectories of $E$ are in high degeneracy and that of $q$ separate somewhat. However, the $\Lambda$CDM model is confounded with ERDE in both of these two cases. $S_3^{(1)}$ and $S_4^{(1)}$, especially the former, perform much better. They can differentiate well only varieties of cases within ERDE except $\Lambda$CDM in the low-redshift region. For high-redshift region, combinations $\{S_n^{(1)},\epsilon\}$ can break the degeneracy. Both of $\{S_3^{(1)},\epsilon\}$ and $\{S_4^{(1)},\epsilon\}$ have the ability to discriminate ERDE with $\alpha=1$ from $\Lambda$CDM, of which the degeneracy cannot be broken by all the before-mentioned parameters. For the case of variable $\beta$ and constant $\alpha$, $S_3^{(1)}(z)$ and $S_4^{(1)}(z)$ can only discriminate ERDE from $\Lambda$CDM. Nothing but pairs $\{S_3^{(1)},\epsilon\}$ and $\{S_4^{(1)},\epsilon\}$ can discriminate not only within ERDE but also ERDE from $\Lambda$CDM. Finally we find that $S_3^{(1)}$ is surprisingly a better choice to discriminate within ERDE itself, and ERDE from $\Lambda$CDM as well, rather than $S_4^{(1)}$.