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    Statefinder hierarchy exploration of the extended Ricci dark energy

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    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 α\alpha and β\beta. By adjusting them, we plot evolution trajectories of some typical parameters, including Hubble expansion rate EE, deceleration parameter qq, the third and fourth order hierarchy S3(1)S_3^{(1)} and S4(1)S_4^{(1)} and fractional growth parameter ϵ\epsilon, respectively, as well as several combinations of them. For the case of variable α\alpha and constant β\beta, in the low-redshift region the evolution trajectories of EE are in high degeneracy and that of qq separate somewhat. However, the Λ\LambdaCDM model is confounded with ERDE in both of these two cases. S3(1)S_3^{(1)} and S4(1)S_4^{(1)}, especially the former, perform much better. They can differentiate well only varieties of cases within ERDE except Λ\LambdaCDM in the low-redshift region. For high-redshift region, combinations {Sn(1),ϵ}\{S_n^{(1)},\epsilon\} can break the degeneracy. Both of {S3(1),ϵ}\{S_3^{(1)},\epsilon\} and {S4(1),ϵ}\{S_4^{(1)},\epsilon\} have the ability to discriminate ERDE with α=1\alpha=1 from Λ\LambdaCDM, of which the degeneracy cannot be broken by all the before-mentioned parameters. For the case of variable β\beta and constant α\alpha, S3(1)(z)S_3^{(1)}(z) and S4(1)(z)S_4^{(1)}(z) can only discriminate ERDE from Λ\LambdaCDM. Nothing but pairs {S3(1),ϵ}\{S_3^{(1)},\epsilon\} and {S4(1),ϵ}\{S_4^{(1)},\epsilon\} can discriminate not only within ERDE but also ERDE from Λ\LambdaCDM. Finally we find that S3(1)S_3^{(1)} is surprisingly a better choice to discriminate within ERDE itself, and ERDE from Λ\LambdaCDM as well, rather than S4(1)S_4^{(1)}.Comment: 8 pages, 14 figures; published versio
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