Abstract
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 B_{text {seed}}sim {10^{24}} G at 5 pc scale, we obtain a CMF in EC of the order of 10^{-10} 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^{+}. Chiral effects on general relativity may lead to strong magnetic fields of the order of sim {10^{18}} G at the early universe resulting from pure metric effects. Strong magnetic fields of the order of B_{text {metric}-text {torsion}}sim {10^{8}} 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} 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.
Highlights
In the case of massless chiral fermions, i.e., neutrino–anti-neutrinos, bouncing cosmology is in order on a Ricci-flat spacetime bubble of electroweak type as in the paper of Enqvist and Olesen [15], where torsion-driven dynamo amplification is used
As in the case of magnetars where Sigl et al have obtained a damping as well on the magnetic fields, showing that the strong magnetic fields of magnetars cannot be explained by chiral dynamos from virtual pairs of electrons and positrons, we show that a torsion chiral current in this case damps the magnetic field of the universe in much the same way as is done in stars
In the massless chiral anomaly fermions the FRW cosmological equations are used in this bubble solution in Ricci-flat spacetime to show that the evolution of this isotropic expansion endowed with magnetic fields may produce a bouncing cosmological solution with electroweak bubbles as considered by Enqvist and Olesen
Summary
J. C (2018) 78:530 this bounce [14] and this is shown in the case of EWPT. The plan of the paper is as follows: In Sect. the massless chiral fermions are shown to be responsible for the driven bouncing cosmological model amplification of the magnetic fields. In the second case the chiral massive fermions of the chiral anomaly currents QED is shown to produce an attenuation of the magnetic field. the chiral dynamo equation is presented in the EC framework, and in Sect. Spin effects become dominant in the early universe in the Einstein–Cartan cosmology bouncing model as we shall see next.
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