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 measures (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 several tens of FRB/GRB systems potentially detected in a decade or so, one may reach reasonable constraints on wCDM models. When combined with Type Ia supernova (SN Ia) data, unprecedented constraints on the 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 IGM(z)> and luminosity distance (D _L(z)) is insensitive to dark energy models. This gives the prospect of applying SN Ia data to calibrate 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.