Abstract It is well known that in torsion theories, constant fermion condensates may create axial currents in vacuum. Here, we show that domain walls in Einstein–Cartan (EC) gravity induce weak torsion couplings on the order of 10^-4 10 - 4 from a magnetic field of 10^-9 \, Gauss 10 - 9 G a u s s and an axial torsion of 10^-32\, GeV 10 - 32 G e V. An example is given where gravitational waves (GWs) induced by teleparallel oscillations of a double cosmic wall system are generated between fermion condensates around a domain wall with external magnetic and torsion fields, and we find that the domain wall thickness depends on torsion. In the case of a thin domain wall, the torsion is proportional to the external magnetic field at the domain wall. This implies that the external torsion of the domain wall helps to polarize the magnetic moments or spins in EC gravity, a process similar to one that was shown recently by the author (Annals of Phys, 2021). Dark energy is considered to be confined between two teleparallel domain walls. The surface density of domain walls decreases with strong spin–torsion density. A fermion condensate with matching EC conditions is given. When two cosmic double walls coalesce, we obtain a constraint between axial torsion and magnetic fields which determines the coupling torsion gₓ g T. For zero modes, k=0 k = 0 and the fermion condensate is constant, when using the constraints between magnetic and torsion fields. A simple cosmological solution can be obtained from the Aliberti and Lambiase solutions within the Einstein–Cartan–Holst framework by calculating the Barbrro–Immirzi parameter β → ∞.
L. C. Garcia de Andrade (Thu,) studied this question.