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