Cosmology-independent estimate of the fraction of baryon mass in the IGM
  from fast radio burst observations
  The excessive dispersion measure (DM) of fast radio bursts (FRBs) has been
proposed to be a powerful tool to study intergalactic medium (IGM) and to
perform cosmography. One issue is that the fraction of baryons in the IGM,
$f_{\rm IGM}$, is not properly constrained. Here we propose a method of
estimating $f_{\rm IGM}$ using a putative sample of FRBs with the measurements
of both DM and luminosity distance $d_{\rm L}$. The latter can be obtained if
the FRB is associated with a distance indicator (e.g. a gamma-ray burst or a
gravitational wave event), or the redshift $z$ of the FRB is measured and
$d_{\rm L}$ at the corresponding $z$ is available from other distance
indicators (e.g. type Ia supernovae) at the same redshift. Since $d_{\rm
L}/{\rm DM}$ essentially does not depend on cosmological parameters, our method
can determine $f_{\rm IGM}$ independent of cosmological parameters. We
parameterize $f_{\rm IGM}$ as a function of redshift and model the DM
contribution from a host galaxy as a function of star formation rate. Assuming
$f_{\rm IGM}$ has a mild evolution with redshift with a functional form and by
means of Monte Carlo simulations, we show that an unbiased and
cosmology-independent estimate of the present value of $f_{\rm IGM}$ with a
$\sim 12\%$ uncertainty can be obtained with 50 joint measurements of $d_{\rm
L}$ and DM. In addition, such a method can also lead to a measurement of the
mean value of DM contributed from the local host galaxy.
