Growth of matter perturbations in the extended viscous dark energy models

In this work, we study the extended viscous dark energy models in the context of matter perturbations. To do this, we assume an alternative interpretation of the flat Friedmann-Lema\^itre-Robertson-Walker Universe, through the nonadditive entropy and the viscous dark energy. We implement the relativistic equations to obtain the growth of matter fluctuations for a smooth version of dark energy. As result, we show that the matter density contrast evolves similarly to the $\Lambda$CDM model in high redshift; in late time, it is slightly different from the standard model. Using the latest geometrical and growth rate observational data, we carry out a Bayesian analysis to constrain parameters and compare models. We see that our viscous models are compatible with cosmological probes, and the $\Lambda$CDM recovered with a $1\sigma$ confidence level. The viscous dark energy models relieve the tension of $H_0$ in $2 \sim 3 \sigma$. Yet, by involving the $\sigma_8$ tension, some models can alleviate it. In the model selection framework, the data discards the extended viscous dark energy models.