Fermionic cosmological model with gauge and Schutz couplings: Classical and quantum analysis

Abstract

A cosmological model for the early universe is investigated where a Schutz fluid and a fermionic field coupled to a gauge field are the sources of the gravitational field. The determination of the scale factor in the classical analysis follows from the Hamiltonian formulation together with Dirac’s method for constrained systems. The expectation value of the scale factor in the quantum analysis is determined from the Wheeler–DeWitt equation. The singularity in the classical solution for the scale factor is avoided in the quantum solution where a bouncing from a minimum value of the scale factor is present. It is shown that: (i) the minimum value of the scale factor depends on the ratio of the fermionic coupling constant and the mass of the vectorial field; (ii) the classical and quantum solutions coincide for large values of the conformal time due to a dilution of the quantum effects with the time evolution; (iii) the behavior of the wave function probability density confirms that the maximum probability occurs when the scale factor has its minimum value equal to its expectation value; (iv) the quantum potential in the Bohmian formulation goes to infinity when the scale factor tends to zero avoiding the singularity at this point.