The $\mu$-deformed Einstein field equations with $\mu$-dependent effective cosmological constant

In this paper, we derive the $\mu$-deformed Einstein field equations from the generalized thermodynamic functions of the $\mu$-deformed analog of Bose gas model, applying the (adapted) Verlinde's approach. The basic role of deformation parameter is shown: it provides the possibility to vary the value of the cosmological constant. Due to this, we suggest an interesting treatment of the cosmological constant (CC) problem within the framework of $\mu$-deformation. Namely, viewing the derived $\mu$-deformed CC as an effective one and varying the parameter $\mu$ appropriately, we gain the possibility to drastically reduce the CC, so as to get for it the realistic value. The relation to dark matter is of importance.