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

Abstract: 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 $\Lambda$CDM 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 $\Lambda$CDM can be distinguished well from each other at the present epoch by using the composite diagnostic ${\epsilon(z), S^{(1)}_{5}}$. Using other combinations, such as ${S^{(1)}_{3}, S^{(1)}_4}$, ${S^{(1)}_{3}, S_{5}}$, ${\epsilon(z), S^{(1)}_{3}}$, and ${\epsilon(z), S_4 }$, some of these five dark energy models cannot be distinguished.