Statefinder hierarchy exploration of the extended Ricci dark energy

Fei Yu; Jing-Lei Cui; Jing-Fei Zhang; Xin Zhang

doi:10.1140/epjc/s10052-015-3505-7

EPJ

Statefinder hierarchy exploration of the extended Ricci dark energy

Fei Yu¹^*, Jing-Lei Cui², Jing-Fei Zhang² and Xin Zhang²^,3

¹ College of Sciences, Shenyang Aerospace University, Shenyang, 110136, China
² Department of Physics, College of Sciences, Northeastern University, Shenyang, 110004, China
³ Center for High Energy Physics, Peking University, Beijing, 100080, China

Received: 23 April 2015
Accepted: 2 June 2015
Published online: 23 June 2015

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 the Hubble expansion rate E, deceleration parameter q, the third- and fourth-order hierarchy $S_3^{(1)}$ and $S_4^{(1)}$ , and the 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 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 the 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 $S_4^{(1)}$ .

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EPJ

Statefinder hierarchy exploration of the extended Ricci dark energy

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