Efeitos não-comutativos em modelos cosmológicos Bianchi I

Abstract

This dissertation investigates the effects of noncommutativity in Bianchi I-type cosmological models, with an emphasis on their implications for the dynamics of expansion and isotropization of the universe. The study is set within the context of extensions to General Relativity, aiming to explore phenomena associated with both the primordial and present-day universe. The approach employs the ADM (Arnowitt-Deser-Misner) Hamiltonian formulation for the geometric sector and the Schutz formalism for the matter sector, introducing noncommutativity either through a deformation of the Poisson bracket algebra or via the generalized Faddeev–Jackiw symplectic formalism. Two main Bianchi I-type models were analyzed: the model with a radiation fluid, relevant to the primordial universe, and the model with a reduced relativistic gas, representing an intermediate phase between radiation and dust. Numerical solutions were used to compare commutative and noncommutative versions, and estimates of noncommutative parameters were derived based on observational data. The results indicate that noncommutativity can influence the dynamics of the primordial universe, affecting the expansion rate and isotropization time, and leaving imprints on cosmological parameters of the present-day universe.