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.
