Bounding the photon mass with gravitationally lensed fast radio bursts
The gravitational time delays of macro-lenses 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 $Δt$ and the leading-to-trailing flux ratio $R$ of strongly lensed fast radio bursts (FRBs). Using the observed values of $Δt$ 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 $m_γ< 5.3 \times {10}^{-42}\,\rm kg$, for a given external shear strength of $γ' = 0.01$, and $m_γ < 2.1 \times 10^{-41}-2.4 \times 10^{-42}\,\text{kg}$, within the external shear range of $0<γ'<1$. 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.