Cosmology with fermionic sources and relativistic fluid in Schutz’s formalism: Classical and quantum solutions

摘要

In this work, a model for the pre-inflationary universe is developed where the sources of the gravitational field are a relativistic fluid and a self-interacting fermionic field. The inclusion of the relativistic fluid is based on Schutz’s model. From the classical analysis based on the Hamiltonian formalism, 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 function of the conformal time is obtained. From the Wheeler–DeWitt equation, the expected value for the scale factor as function of the conformal time is determined. It is shown that contrary to the classical solution, the expected value of the scale factor does not have a singularity, since it is preceded by a contracted phase up to a minimum value from which the universe begins to expand. Furthermore, from the plots of the classical and quantum solutions for the scale factor as functions of the conformal time it is shown that a decoherence of the quantum solution occurs for late times and both solutions coincide.