Modelo cosmológico com fontes fermiônicas e fluido relativístico no formalismo de Schutz: uma analise clássica e quântica

Abstract

In this work we propose a cosmological model for the eaarly universe, where the relativistic Schutz fluid and the fermionic field take the role of the source for the gravitational field. From the classical analysis, based on hamiltonian formalism together with Dirac’s method for constrained systems, it is shown that the fluid degrees of freedom can be embodied by a conformal time variable, and an expression for the scale factor as a funtion of the conformal time is obteined. The expected value for the scale factor in quantum analysis, is determined by the Wheeler-De Witt equations. The singularity in the classical solution can be avoided on the quantum solution, which have a minimum value for the scale factor, from which the universe begins to expand, and according to the evolution of time the quantum effects are diluted, resulting for hight levels of conformal time, the quantum and classical solutions coincide. Finishing our analysis with Bohm formulation in quantum mechanics, we can see that the quantum potential assume high values when scale factor goes to zero, confirming again that the singularity can be avoided.