Quantum Bohmian description of a primordial universe with Fermionic and Bosonic sources

Abstract

We present a model of an early universe where the sources of gravitational effects are a scalar field, a relativistic fluid based on Schutz’s model and a self-interacting fermionic field. From the classical analysis based on the Hamiltonian formalism we show that the scale factor of the universe can be expressed in terms of a conformal time that emerges from the fluid’s degrees of freedom. From the Wheeler–DeWitt equation, a wave packet solution as function of the conformal time is determined. It is shown that the combination of the scalar and the fermionic field furnishes a consistent quantum regime and a smooth transition to the classical description, working with the aid of the Bohmian mechanics and in particular with the concept of quantum potential. The influence of the presence of the scalar field is also discussed.