Photon mass limits driven by axions, Lorentz violation, chiral and gravitational anomalies in non-Riemannian spaces, and helical dynamo seeds

Abstract

In this paper two types of applications of Cartan torsion to cosmology and quantum field theory are given. The first is given by massive photon axial torsion mixing through non-minimal coupling. It is shown that chiral anomalies induce upper limits on the photon mass and galactic dynamo seeds. In this example we obtain magnetic field seeds of the order of 10−16 G from a strong chiral battery magnetic field of the order of 1030 G. This cosmic magnetic field is in accordance with previous magnetic dynamo seed limits as 10−22 G ≤ Bseed ≤ 10−12 G given by Barrow et al. (Phys. Rev. D, 86, 023533 (2012). doi: 10.1103/PhysRevD.86.023533 ). In this example, as in the Prokopec et al. (Phys. Rev. Lett. 89, 101301 (2002). doi: 10.1103/PhysRevLett.89.101301 ) torsionless case, which associates Dolgov anomalies to photon mass limits, we show that at early universe scales, 10−32 eV is a very stringent limit. Here we can show that the parameter [Formula: see text], which is well within the lower bound of r needed for the magnetic field to seed galactic dynamos. Helical magnetic fields are obtained. One can also derive massive photon limits from axial chiral anomalies with torsion degrees of freedom (Duncan et al. Nucl. Phys. B, 387, 215 (1992). doi: 10.1016/0550-3213(92)90052-D ) leading to photon mass of the order of 10−11 eV. Dynamo equations are obtained from anomalous Maxwell equations as well as magnetic wave equations with photon mass, which are analytically solved. In the second example one shows that Chern–Simons (CS) current is affected by the presence of minimal coupled torsion. In this case as well one obtains a photon mass limit of the order 10−18 eV. Gravitational anomalies in Riemann–Cartan spacetime with axial torsion are also obtained. Recently, Terrano et al. (Phys. Rev. Lett. 122, 231301 (2019). doi: 10.1103/PhysRevLett.122.231301 ) computed dark matter mass constraints of the order of 10−23 eV from spin-polarised torsion balances, which has given some support for torsion theories of Einstein–Cartan type. Here, however, we deal with torsion with dynamical degrees of freedom. Lorentz violation in non-Riemannian CS currents are investigated.