Einstein-Cartan-Holst-Proca Dynamos Massive Photons as Dark Matter and GWs

In this paper we extend Shaposhnikov et al parity violating Einstein-Cartan-Holst action by adding to Holst term H, a Proca photontorsion coupling χpt = 10−24 as computed by De Sabbata, Garcia de Andrade, and Sivaram. The strenght of Holst term is obtained, in the case of early universe torsion as T ∼ 1MeV gravity part is the Planck mass product with the Holst term. The photon mass in this case yields m2 γH ∼ 10−69GeV4. Therefore in the case, photon interacts very weakly with spin-torsion matter in Einstein-Cartan gravity, the strength of Maxwell-Proca-Holst interaction is much weaker than pure gravity sector. For dark photons this situation changes drastically since a dark photon mass reaches 1.5GeV , and from this mass and T = 10−3GeV , one obtains a Maxwell-Proca-Holst strenght of 10−6GeV 4, which is now comparable with the gravity sector. Dynamo mechanism competes with the chirality and dissipation by the handness of the magnetic field with respect to torsion trace vector, to regenerate the magnetic field decay. Bombacigno and Mantovani have recently found a sign of the Immirzi parameter in the Holst-Nieh-Yan extension of EC gravity. Here we also find torsion waves for the Immirzi inverse parameter and in the sense that this divergence of torsion trace is porportional to Immirzi field.].