Modelos cosmológicos não comutativos com paredes de domínio

Abstract

The aim of this work is to study noncommutative cosmological models, in which noncommutativity is inserted as an alternative explanation for the accelerated expansion of the Universe. In the current universe, such noncommutativity would be a remnant of a primordial universe where quantum interactions imposed a noncommutative geometry on space-time. The models were built based on the ADM formalism and the Schutz formalism to develop a Hamiltonian formulation of the theory of general relativity coupled to a perfect fluid. To this end, 4-dimensional space-time is foliated by 3-dimensional spatial hypersurfaces separated from time, represented by a scalar field and a vector field, and fluid dynamics are described by scalar fields called velocity potentials. The fluid coupled to the theory will be formed by domain walls, topological defects generated by spontaneous symmetry breaking during phase transitions in the early universe. Respecting the cosmological principle, the universe is described by the Friedmann-Robertson-Walker metric and, in the Hamiltonian formulation, noncommutativity is introduced into the algebra of Poisson brackets through the so-called noncommutative parameter. Finally, there are obtained equations of motion and the respective resulting models. Those will be analyzed for different values of the parameters involved in order to determine how these parameters influence the behavior of the scale factor function and whether noncommutativity favors the accelerated expansion of the universe or not.