Photon Mass Limits from Fast Radio Bursts
  The frequency-dependent time delays in fast radio bursts (FRBs) can be used
to constrain the photon mass, if the FRB redshifts are known, but the
similarity between the frequency dependences of dispersion due to plasma
effects and a photon mass complicates the derivation of a limit on $m_\gamma$.
The dispersion measure (DM) of FRB 150418 is known to $\sim 0.1$%, and there is
a claim to have measured its redshift with an accuracy of $\sim 2$%, but the
strength of the constraint on $m_\gamma$ is limited by uncertainties in the
modelling of the host galaxy and the Milky Way, as well as possible
inhomogeneities in the intergalactic medium (IGM). Allowing for these
uncertainties, the recent data on FRB 150418 indicate that $m_\gamma \lesssim
1.8 \times 10^{-14}$eV c$^{-2}$ ($3.2 \times 10^{-50}$kg), if FRB 150418 indeed
has a redshift $z = 0.492$ as initially reported. In the future, the different
redshift dependences of the plasma and photon mass contributions to DM can be
used to improve the sensitivity to $m_\gamma$ if more FRB redshifts are
measured. For a fixed fractional uncertainty in the extra-galactic contribution
to the DM of an FRB, one with a lower redshift would provide greater
sensitivity to $m_\gamma$.
