Bounding the photon mass with cosmological propagation of fast radio bursts

Photon is the fundamental quantum of electromagnetic fields, whose mass, $m_{\gamma}$, should be strictly zero in Maxwell's theory. But not all theories adopt this hypothesis. If the rest mass of the photon is not zero, there will be an additional time delay between photons of different frequencies after they travel through a fixed distance. By analyzing the time delay, we can measure or constrain the photon mass. Fast radio bursts (FRBs) -- transient radio bursts characterized by millisecond duration and cosmological propagation -- are excellent astrophysical laboratories to constrain $m_{\gamma}$. In this work we use a catalog of 129 FRBs in a Bayesian framework to constrain $m_{\gamma}$. As a result, we obtain a new bound on the photon mass, $m_{\gamma} \leq 3.1\times 10^{-51}\rm\,kg\simeq 1.7 \times 10^{-15}\,eV/c^2$ ($m_{\gamma} \leq 3.9\times 10^{-51}\rm\,kg \simeq 2.2 \times 10^{-15}\,eV/c^2$) at the $68\%$ $(95\%$) confidence level. The result represents the best limit purely from kinematic analysis of light propagation. The bound on the photon mass will be tighter in the near future with increment in the number of FRBs, more accurate measurement of the redshift for FRBs, and refinement in the knowledge about the origin of dispersion measures (DMs).