Fast radio bursts as a cosmic probe?
  We discuss the possibility of using fast radio bursts (FRBs), if
cosmological, as a viable cosmic probe. We find out that the contribution of
the host galaxies to the detected dispersion measures can be inapparent for the
FRBs not from galaxy centers or star forming regions. The inhomogeneity of the
intergalactic medium (IGM), however, causes significant deviation of the
dispersion measure from that predicted in the simplified homogeneous IGM model
for individual event. Fortunately, with sufficient FRBs along different
sightlines but within a very narrow redshift interval (e.g., $\Delta z \sim
0.05$ or $\Delta z \sim 0.05(1+z)$), the mean from averaging observed
dispersion measures does not suffer such a problem and hence may be used as a
cosmic probe. We show that in the optimistic case (e.g., tens FRBs in each
$\Delta z$ have been measured; the most distant FRBs were at redshift $\geq 3$;
the host galaxies and the FRB sources contribute little to the detected
dispersion measures) and with all the uncertainties (i.e. the inhomogeneity of
the IGM, the contribution and uncertainty of host galaxies as well as the
evolution and error of $f_{\rm IGM}$) considered, FRBs could help constrain the
equation of state of dark energy.
