Extracting host galaxy dispersion measure and constraining cosmological
  parameters using fast radio burst data
  The excessive dispersion measures (DMs) and high Galactic latitudes of fast
radio bursts (FRBs) hint toward a cosmological origin of these mysterious
transients. Methods of using measured DM and redshift $z$ to study cosmology
have been proposed, but one needs to assume a certain amount of DM contribution
from the host galaxy (DM$_{\rm HG}$) in order to apply those methods. We
introduce a slope parameter $\beta(z) \equiv d \ln \left< {\rm DM}_{\rm E}
\right> / d \ln z$ (where DM$_{\rm E}$ is the observed DM subtracting the
Galactic contribution), which can be directly measured when a sample of FRBs
have $z$ measured. We show that $\left< {\rm DM_{HG}}\right>$ can be roughly
inferred from $\beta$ and the mean values, $\overline{\rm \left<DM_{\rm
E}\right>}$ and $\bar z$, of the sample. Through Monte Carlo simulations, we
show that the mean value of local host galaxy DM,
$\left<\rm{DM_{HG,loc}}\right>$, along with other cosmological parameters (mass
density $\Omega_m$ in the $\Lambda$CDM model, and the IGM portion of the baryon
energy density $\Omega_b f_{\rm IGM}$) can be independently measured through
MCMC fitting to the data.
