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 of
the observed frequency, i.e., dispersion measure. Therefore, FRBs provide one
of the ideal laboratories to test Einstein's weak equivalence principle (WEP):
the hypothetical time lag between photons with different energies under a
gravitational potential. If WEP is violated, such evidence should be exposed
within the observational uncertainties of dispersion measures, unless the WEP
violation also depends on the inverse-square of the observed frequency. In this
work, we constrain the difference of gamma parameters ($\Delta\gamma$) between
photons with different energies using the observational uncertainties of FRB
dispersion measures, where $\Delta\gamma=0$ for Einstein's general relativity.
Adopting the averaged 'Shapiro time delay' for cosmological sources, FRB 121002
at $z=1.6\pm0.3$ and FRB 180817.J1533+42 at $z=1.0\pm0.2$ place the most
stringent constraints of $\log\Delta\gamma<-20.8\pm0.1$ and
$\log(\Delta\gamma/r_{E}) < -20.9\pm0.2$, respectively, where $r_{E}$ is the
energy ratio between the photons. The former is about three orders of magnitude
lower than those of other astrophysical sources in previous works under the
same formalization of the Shapiro time delay while the latter is comparable to
the tightest constraint so far.
