Discriminating dark energy models by using the statefinder hierarchy and the growth rate of matter perturbations

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We apply the Statefinder hierarchy and the growth rate of matter perturbations to discriminate modified Chaplygin gas (MCG), generalized Chaplygin gas (GCG), superfluid Chaplygin gas (SCG), purely kinetic k-essence (PKK), and ΛCDM model. We plot the evolutional trajectories of these models in the statefinder plane and in the composite diagnostic plane. We find that GCG, MCG, SCG, PKK, and ΛCDM can be distinguished well from each other at the present epoch by using the composite diagnostic {ε(z), S⁽¹⁾₅}. Using other combinations, such as {S⁽¹⁾₃, S⁽¹⁾₄}, {S⁽¹⁾₃, S₅}, {ε(z), S⁽¹⁾₃}, and {ε(z), S₄ }, some of these five dark energy models cannot be distinguished.