Non Commutative Bianchi type II Quantum Cosmology

In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler-DeWitt equation for any factor ordering, to the anisotropic Bianchi type II cosmological model are found, using a stiff fluid ($\gamma =1$). In our toy model, we introduce noncommutative scale factors, is say, we consider that all minisuperspace variables ${\mathrm{q}}^{\mathrm{i}}$ does not commute, so the simplectic structure was modified.