Constraining the epoch of reionization with highly dispersed fast radio bursts

The period in which hydrogen in the intergalactic medium (IGM) is ionized, known as the epoch of reionization (EoR), is still poorly understood. The timing and duration of the EoR is expected to be governed by the underlying astrophysics. Furthermore, most models of reionization predict a correlation between the density and ionization field. Here we consider using the mean dispersion measure (DM) of high redshift fast radio bursts (FRBs) as a probe of the underlying astrophysics and morphology of the EoR. To do this, we forecast observational scenarios by building mock data sets of non-repeating FRBs between redshifts 8 ≤ z ≤ 10. In our forecasts we assume a fiducial inside-out reionization scenario with midpoint of reionziation z = 2.0, and duration (i.e. the duration between mean ionized fraction of 0.25 to 0.75) Δz = 7.8. It is assumed that all FRBs have accompanying spectroscopic redshift measurements. We find that samples of 100 high redshift FRBs, in the above mentioned narrow redshift range, can rule out uncorrelated reionization at 68 per cent credibility, while larger samples, ≥10⁴ FRBs, can rule out uncorrelated reionization at $95{{\ \rm per\ cent}}$ credibility. We also find 100 high redshift FRBs can rule out scenarios where the Universe is entirely neutral at z = 10 with $68{{\ \rm per\ cent}}$ credibility. Further, with ≥10⁵ FRBs, we can constrain the duration Δz of reionization to $\Delta z = 2.0^{+0.5}_{-0.4}$ and the midpoint of reionization to $z = 7.8^{+0.4}_{-0.2}$ at 95 per cent credibility.