Upper limits on Einstein’s weak equivalence principle placed by uncertainties of dispersion measures of fast radio bursts

Fast radio bursts (FRBs) are astronomical transients with millisecond timescales occurring at cosmological distances. The observed time lag between different energies of each FRB is well described by the inverse-square law frequency, i.e., dispersion measure. Therefore, FRBs provide one ideal laboratories to test Einstein's weak equivalence principle (WEP): hypothetical photons under a gravitational potential. If WEP violated, such evidence should be exposed within observational uncertainties measures, unless violation also depends on frequency. In this work, we constrain difference gamma parameters ($\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}$) using where $\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}=0$ for general relativity. Adopting averaged `Shapiro delay' sources, 121002 $z=1.6\ifmmode\pm\else\textpm\fi{}0.3$ and $180817.\mathrm{J}1533+42$ $z=1.0\ifmmode\pm\else\textpm\fi{}0.2$ place most stringent constraints $\mathrm{log}\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}<\ensuremath{-}20.8\ifmmode\pm\else\textpm\fi{}0.1$ $\mathrm{log}(\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}/{r}_{E})<\phantom{\rule{0ex}{0ex}}\ensuremath{-}20.9\ifmmode\pm\else\textpm\fi{}0.2$, respectively, ${r}_{E}$ energy ratio photons. former about three orders magnitude lower than those other astrophysical sources in previous works same formalization Shapiro delay while latter comparable tightest constraint so far.