Photon mass new limits from strong photon-torsion coupling generation of primordial magnetic fields

Abstract: Recently Adelberger et al [Phys Rev Lett 98: 010402, (2007)] have placed a limit to photon mass by investigating the primordial magnetic fields. Earlier Bertolami et al [Phys Lett \textbf{B} 455, 96(1999)] showed that massive photons in a spontaneous Lorentz breaking may generate primordial magnetic fields consistent with galactic dynamo seeds. Torsion coupling constant of order $10^{-5}$, much higher than the previously obtained by de Sabbata and Sivaram of $10^{-24}$, leads to strong amplification of magnetic field able to seed galactic dynamo at recombination era contrary to what happens in general relativistic dynamos. This results in $B\sim{10^{-5}{\beta}G}$ where ${\beta}$ is the massive photon-torsion coupling. Thus in order to obtain the observed galaxy field of $B_{G}\sim{{\mu}G}$ one should have a coupling $\beta\sim{10^{-1}}$, never observed in the universe. Thus we may conclude that the weaker couplings for torsion to e.m fields shall only produce magnetic fields without dynamos starting from extremely strong magnetic seeds. From the strongest photon-torsion considered one obtains the best CMB estimate for torsion generated magnetic fields $\frac{{\delta}B}{B}\le{10^{-4}}$. By making use of the strong photon-torsion limits obtained here, photon mass limit of $m_{\gamma}\sim{10^{-24}eV}$, well-within limits found in literature, which allows us to conclude that a stronger massive photon-torsion limit is physically consistent. Actually this last limit is also graviton mass limit. This results differs from Adelberger et al by two orders of magnitude.