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In this paper, the viscous cosmological dynamics are studied in the presenceof dark matter Bose-Einstein Condensation (BEC) by curved-FRW background. Forthis purpose, we use the BEC regime rather than the normal dark matter (thecold dark matter or the barotropic dark matter) with the dark matter Equationof State (EoS) as $p_{dm} \propto \rho_{dm}^2$, which arises from thegravitational form. Therefore, we obtain the corresponding continuity equationswith the existence of the universe components by considering an interactingmodel with modified Chaplygin gas. Afterward, we derive the energy density andthe pressure of dark energy in terms of the redshift parameter. And then, byintroducing a parametrization function and fitting it with 51 supernova datawith the likelihood analysis, we find the cosmological parameters versusredshift parameter. In what follows, we plot the corresponding dynamic graphsproportional to redshift, and then we represent the universe is currentlyundergoing an accelerated expansion phase. Finally, we explore the stabilityand the instability of the present model with the sound speed parameter.

Viscous interacting and stability on dark matter Bose-Einstein condensation with modified Chaplygin gas