Noncommutative Bianchi I and III Cosmology Models: Radiation Era Dynamics and γ Estimation

In this work, we analyze the dynamical evolution of locally rotationally symmetric anisotropic cosmological models of Bianchi type I (flat curvature) and Bianchi type III (open curvature) within a noncommutative phase space framework characterized by a deformation parameter γ. Using a Hamiltonian formulation based on Schutz’s formalism for a perfect radiation fluid, we introduce noncommutative Poisson brackets that allow for geometric corrections to commutative dynamics. The resulting equations are solved numerically, which allows for the study of the impact of γ and the energy density C on the expansion of the universe and the evolution of anisotropy. The results show that γ<0 improves expansion and favors isotropization, while γ>0 tends to slow expansion and preserve residual anisotropy, especially in the open curvature model. It is estimated that the influence of noncommutativity was significant during the early stages of the universe, decreasing toward the present time, suggesting that this approach could serve as an effective alternative to the cosmological constant in describing the evolution of the early universe.