Addendum to: Dynamical torsion suppression in Brans–Dicke inflation and Lorentz violation (Eur Phys J C (2022)): Einstein–Cartan–Brans–Dicke–Maxwell universe with a chiral dynamo?

We have recently shown that in Einstein–Cartan–Brans–Dicke (ECBD) gravity, torsion effects are not present in today’s universe because they are suppressed in a four-dimensional system, as in the bulk of five-dimensional braneworld endowed with torsion. In this addendum, we naturally introduce new features on the ECBD Maxwell Lagrangian dynamics deriving the chiral dynamo equation, and studying its physical properties. Magnetogenesis results are derived in this ECBDM universe. In particular we show, in the present universe, torsional magnetic fields of the second-order in the ohmic resistivity behave as $$B_{{\text {ECBD}}}=10^{-13}$$ B ECBD = 10 - 13 Gauss, which is exactly the estimate made by Miniati et al. (Phys Rev Lett, 2018) for the axion QCD magnetic field in the present universe. We found this at 1 pc coherent length, whereas they found it at 20 pc . To obtain this result, we consider a strong magnetic field of the order of the Biermann battery $$10^{30}G$$ 10 30 G . This seems to show that our model of ECBDM gravity can be used with success in inflationary magnetogenesis with torsion. Inflation or deflation are shown to depend upon torsion chirality. Torsion is shown to depend upon the BD parameter $${\omega }$$ ω and decays in time as in the reference to which this addendum refers (Garcia de Andrade in Eur Phys J C, 2002).