Bounding the photon mass with gravitationally lensed fast radio bursts

The gravitational time delays of macrolenses can be used to constrain the rest mass of the photon with high accuracy. Assuming a point mass + external shear lens model, we prove that an upper limit of the photon mass can be derived directly from two observables---the time delay $\mathrm{\ensuremath{\Delta}}t$ and the leading-to-trailing flux ratio $R$ of strongly lensed fast radio bursts (FRBs). Using the observed values of $\mathrm{\ensuremath{\Delta}}t$ and $R$ of a lensed FRB candidate, i.e., FRB 20190308C, as a reference, we obtain a strict upper limit of the photon mass between ${m}_{\ensuremath{\gamma}}<5.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}42}\text{ }\text{ }\mathrm{kg}$, for a given external shear strength of ${\ensuremath{\gamma}}^{\ensuremath{'}}=0.01$, and ${m}_{\ensuremath{\gamma}}<2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}41}\ensuremath{-}\phantom{\rule{0ex}{0ex}}2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}42}\text{ }\text{ }\mathrm{kg}$, within the external shear range of $0<{\ensuremath{\gamma}}^{\ensuremath{'}}<1$. This provides the most stringent limit to date on the photon mass through gravitational lensing time delays, improving by 1 to 2 orders of magnitude the previous results obtained from lensed active galactic nuclei.