2014ApJ...783L..35D

If a small fraction of fast radio bursts (FRBs) are associated with gamma-ray bursts (GRBs), as recently suggested by Zhang, the combination of redshift measurements of GRBs and dispersion measure (DM) measurements of FRBs opens a new window to study cosmology. At z < 2 where the universe is essentially fully ionized, detections of FRB/GRB pairs can give an independent measurement of the intergalactic medium portion of the baryon mass fraction, Ω_bf_IGM, of the universe. If a good sample of FRB/GRB associations are discovered at higher redshifts, the free electron column density history can be mapped, which can be used to probe the reionization history of both hydrogen and helium in the universe. We apply our formulation to GRBs 101011A and 100704A that each might have an associated FRB, and constrained Ω_bf_IGM to be consistent with the value derived from other methods. The methodology developed here is also applicable, if the redshifts of FRBs not associated with GRBs can be measured by other means.