Probing Diffuse Gas with Fast Radio Bursts
  The dispersion measure -- redshift relation of Fast Radio Bursts,
$\mathrm{DM}(z)$, has been proposed as a potential new probe of the cosmos,
complementary to existing techniques. In practice, however, the effectiveness
of this approach depends on a number of factors, including (but not limited to)
the intrinsic scatter in the data caused by intervening matter inhomogeneities.
Here, we simulate a number of catalogues of mock FRB observations, and use MCMC
techniques to forecast constraints, and assess which parameters will likely be
best constrained. In all cases we find that any potential improvement in
cosmological constraints are limited by the current uncertainty on the the
diffuse gas fraction, $f_{\rm d}(z)$. Instead, we find that the precision of
current cosmological constraints allows one to constrain $f_{\rm d}(z)$, and
possibly its redshift evolution. Combining CMB + BAO + SNe + $H_0$ constraints
with just 100 FRBs (with redshifts), we find a typical constraint on the mean
diffuse gas fraction of a few percent. A detection of this nature would
alleviate the "missing baryon problem", and therefore highlights the value of
localisation and spectroscopic followup of future FRB detections.
