The Efficiency of CP-Violating <i>α</i>2-Dynamos from Primordial Cosmic Axion Oscillation with Torsion

Abstract

Recently torsion fields were introduced in CP-violating cosmic axion a 2 -dynamos [Garcia de Andrade, Mod Phys Lett A, (2011)] in order to obtain Lorentz violating bounds for torsion. Here instead, oscillating axion solutions of the dynamo equation with torsion modes [Garcia de Andrade, Phys Lett B (2012)] are obtained taking into account dissipative torsion fields. Magnetic helicity torsion oscillatory contribution is also obtained. Note that the torsion presence guarantees dynamo efficiency when axion dynamo length is much stronger than the torsion length. Primordial axion oscillations due to torsion yield a magnetic field of 10 9 G at Nucleosynthesis epoch. This is obtained due to a decay of BBN magnetic field of 10 15 G induced by torsion. Since torsion is taken as 10 –20 s –1 , the dynamo efficiency is granted over torsion damping. Of course dynamo efficiency is better in the absence of torsion. In the particular case when the torsion is obtained from anomalies it is given by the gradient of axion scalar [Duncan et al. , Nuclear Phys B 87, 215] that a simpler dynamo equation is obtained and dynamo mechanism seems to be efficient when the torsion helicity, is negative while magnetic field decays when the torsion is positive. In this case an extremely huge value for the magnetic field of 10 15 Gauss is obtained. This is one order of magnitude greater than the primordial magnetic fields of the domain wall. Actually if one uses t DW ~ 10 - 4 s one obtains B DW ~ 10 22 G which is a more stringent limit to the DW magnetic primordial field.