Considering Verlinde's entropic gravity proposal, we focus on the effects of fermionic q deformation on Einstein's field equations and Friedmann equations. For this purpose, we represent the thermodynamical properties of the deformed fermion gas model in two-dimensional space. To describe the behavior of the quantum black holes, deformed Einstein field equations are derived with the help of the deformed entropy function. Moreover, deformed Friedmann equations are investigated by using Friedmann-Robertson-Walker (FRW) metric. We also present the effective ones of the energy density, the pressure, and the equation of state for the dark energy. Lastly, we derive an analytical expression of the effective density parameter of dark energy.

考虑到 Verlinde 的熵引力提议，我们关注费米子q变形对爱因斯坦场方程和弗里德曼方程的影响。为此，我们在二维空间中表示变形费米子气体模型的热力学性质。为了描述量子黑洞的行为，借助变形熵函数导出变形爱因斯坦场方程。此外，使用弗里德曼-罗伯逊-沃克 (FRW) 度量研究了变形的弗里德曼方程。我们还给出了暗能量的能量密度、压力和状态方程的有效值。最后，我们推导出暗能量的有效密度参数的解析表达式。