Noncommutative effects in Bianchi I cosmology with reduced relativistic gas

In this work, we investigate the effects of phase space noncommutativity on the dynamics of a Bianchi I (BI) cosmological model coupled to a reduced relativistic gas (RRG). The BI model provides a homogeneous but anisotropic framework suitable for exploring the transition from an early anisotropic Universe to the current isotropic stage. The RRG fluid interpolates between radiation and matter regimes, enabling a consistent treatment of the transition from the radiation-dominated to the matter-dominated era. In order to incorporate noncommutativity into the classical equations of motion, we employ the generalized symplectic formalism developed by Faddeev–Jackiw and extended by Barcelos–Wotzasek, which allows the introduction of noncommutative (NC) parameters via deformations in the symplectic structure. Within this approach, we derive a modified Hamiltonian expressed in terms of commutative variables that incorporate all NC effects. We then solve the resulting equations numerically and analyze the behavior of the scale factor and the anisotropic functions under variations of the NC parameters, as well as other physical and initial parameters of the model. Our results show that negative values of the NC parameters increase the expansion rate and reduce the isotropization timescale, partially mimicking the effect of a positive cosmological constant. We also estimate values for the NC parameters by numerically solving the integral expression for the age of the Universe, requiring consistency with observational data from the Planck 2018 mission. These findings support the possibility that noncommutativity may provide a geometric mechanism capable of accounting for the late-time acceleration and isotropization of the Universe, without requiring additional exotic energy components.