Quantized Dirac Fields in torsionful gravity: cosmological implications and links with the dark universe

In this paper, we consider a classical field in square torsion theory as a source of torsion for a quantum fermion field in Friedmann–Lemaître–Robertson–Walker (FLRW) metric. In the framework of QFT, we obtain vacuum contributions to the energy–momentum tensor and to the axial current that modify the dynamics of the classical field and the field equations as back-reaction. These contributions lead to a modified classical field and therefore to a modified torsion term Lμ and expectation value of energy–momentum tensor Tμν on the quantum vacuum, altering the field equations in an interactive process. We consider the first step of this process and we find that the vacuum condensate could affect the inflationary phase of the Universe. Higher-order terms could impact the dark Universe.