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

TL;DR

The paper investigates a semiclassical setup in which a classical square‑torsion gravity sources a quantized Dirac field in a flat FLRW background. The authors diagonalize the torsion‑modified Dirac Hamiltonian via a Bogoliubov transformation, defining a physical vacuum $|0_c(t_0)\rangle$ whose condensate contributes nontrivially to the axial current $L^{\mu}$ and to the energy–momentum tensor $T^{QFT}_{\mu\nu}$, thereby back‑reacting on the classical field. In the strong‑coupling regime, they derive leading contributions to $L^{\mu}$ and $\langle T^{QFT}_{\mu\nu}\rangle$ that scale as $C^{-4}(t)$, with $L^i$ proportional to $\breve{T}^i(t_0)$ and regulated by a UV cutoff $\Lambda$; the vacuum energy density behaves like radiation with $w=1/3$ in the massless limit. The work establishes a framework for iterative back‑reaction, linking the condensate dynamics to the torsion and potential implications for inflation and the dark sector, and sets the stage for more complete analyses of quantum back‑reaction in torsionful cosmologies.

Abstract

We consider a classical field in square torsion theory as a source of torsion for a quantum fermion field in 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 $L^μ$ and expectation value of energy-momentum tensor $T^{μν}$ on the quantum vacuum, altering the field equations in an interative 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.