Fast Radio Burst/Gamma-Ray Burst Cosmography
  Recently, both theoretical arguments and observational evidence suggested
that a small fraction of fast radio bursts (FRBs) could be associated with
gamma-ray bursts (GRBs). If such FRB/GRB association systems are commonly
detected in the future, the combination of dispersion measure (DM) derived from
FRBs and redshifts derived from GRBs makes these systems a plausible tool to
conduct cosmography. We quantify uncertainties in deriving the
redshift-dependent DM_{IGM} as a function of z, and test how well dark energy
models can be constrained with Monte Carlo simulations. We show that with
potentially several 10s of FRB/GRB systems detected in a decade or so, one may
reach reasonable constraints on wCDM models. When combined with SN Ia data,
unprecedented constraints on dark energy equation of state may be achieved,
thanks to the prospects of detecting FRB/GRB systems at relatively high
redshifts. The ratio between the mean value < DM_{IGM} (z)> and luminosity
distance (D_{L} (z)) is insensitive to dark energy models. This gives the
prospects of applying SN Ia data to calibrate < DM_{IGM} (z)> using a
relatively small sample of FRB/GRB systems, allowing a reliable constraint on
the baryon inhomogeneity distribution as a function of redshift. The
methodology developed in this paper can also be applied, if the FRB redshifts
can be measured by other means. Some caveats of putting this method into
practice are also discussed.
