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We propose an approach considering the nonextensive effects in the context ofthe Verlinde theory in order to address an extended cosmological model in thecontext of viscous dark energy. Specifically, this model leads to a tinyperturbation in the dynamics of the expansion of the universe through thegeneralized Friedmann equations so-called the extended $\Lambda$CDM model. Fromthe observational test standpoint, we make a Bayesian analysis of the models ofbulk viscosity for dark energy which follows the Eckart theory of bulkviscosity. These models are investigated through the context of both models$\Lambda$CDM and extended $\Lambda$CDM. The Bayesian analysis is performedusing the data of CMB Distance priors, Baryon Acoustic OscillationsMeasurements, Cosmic Chronometers, and SNe Ia distance measurements.

Extended $\Lambda$CDM model and viscous dark energy: A Bayesian analysis