The effects of q-statistics on cosmology

Abstract: Considering Verlinde's entropic gravity proposal, we focus the effects of fermionic $q$ deformation on the 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 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.