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 $8\leq z \leq 10$. 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 $68\%$ credibility, while larger samples, $\geq
10^4$ FRBs, can rule out uncorrelated reionization at $95\%$ credibility. We
also find 100 high redshift FRBs can rule out scenarios where the Universe is
entirely neutral at $z = 10$ with $68\%$ credibility. Further with $\geq 10^5$
FRBs, we can constrain the duration $\Delta z$ of reionization (duration
between mean ionized fraction 0.25 to 0.75) to $\Delta z = 2.0^{+0.5}_{-0.4}$,
and the midpoint of reionization to $z = 7.8^{+0.4}_{-0.2}$ at $95\%$
credibility.
