Diagnostics and future evolution analysis of the two parametric models

In this paper, we apply three diagnostics including $Om$, Statefinder hierarchy and the growth rate of perturbations into discriminating the two parametric models for the effective pressure with the $Λ$CDM model. By using the $Om$ diagnostic, we find that both the model 1 and the model 2 can be hardly distinguished from each other as well as the $Λ$CDM model in terms of 68\% confidence level. As a supplement, by using the Statefinder hierarchy diagnostics and the growth rate of perturbations, we discover that not only can our two parametric models be well distinguished from $Λ$CDM model, but also, by comparing with $Om$ diagnostic, the model 1 and the model 2 can be distinguished better from each other. In addition, we also explore the fate of universe evolution of our two models by means of the rip analysis.

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