In this work we discuss a general approach for the dissipative dark matter considering a nonextensive bulk viscosity and taking into account the role of generalized Friedmann equations. This generalized $Lambda$CDM model encompasses a flat universe with a dissipative nonextensive viscous dark matter component, following the Eckart theory of bulk viscosity. In order to compare models and constrain cosmological parameters, we perform Bayesian analysis using one of the most recent observations of Type Ia Supernova, baryon acoustic oscillations, and cosmic microwave background data.
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