Metric-torsion decay of non-adiabatic chiral helical magnetic fields against chiral dynamo action in bouncing cosmological models

Metric-torsion effects on chiral massless fermions are investigated in the realm of the adiabatic amplification of cosmological magnetic fields (CMFs) in a general relativistic framework and in the framework of Einstein–Cartan (EC) bouncing cosmologies. In GR the chiral effect is proportional to the Hubble factor and the solution of the dynamo equation leads to an adiabatic magnetic field, while in Einstein–Cartan bouncing cosmology we have non-adiabatic magnetic fields where the breaking of adiabaticity is given by a torsion term. Using a EWPT magnetic field of the order of Bseed∼1024\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_{\text {seed}}\sim {10^{24}}$$\end{document} G at 5 pc scale, we obtain a CMF in EC of the order of 10-10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-10}$$\end{document} G, which is still able to seed a galactic dynamo which amplifies this field up to galactic magnetic fields of four orders of magnitude, which is a mild dynamo. In the case of massive chiral fermions it is shown that torsion actually attenuated the convective dynamo term in the dynamo equation obtained from the QED of an electron–positron pair e-e+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e^{-}e^{+}$$\end{document}. Chiral effects on general relativity may lead to strong magnetic fields of the order of ∼1018\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim {10^{18}}$$\end{document} G at the early universe resulting from pure metric effects. Strong magnetic fields of the order of Bmetric-torsion∼108\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_{\text {metric}-\text {torsion}}\sim {10^{8}}$$\end{document} G may be obtained from very strong seed fields. At 1 Mpc scale of the present universe a galactic dynamo seed of the order of 10-19\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-19}$$\end{document} G is found. It is shown in this paper that chiral dynamo effects in the expanded universe can be obtained if one takes into account the speed of the cosmic plasma.