Detecting Helium Reionization with Fast Radio Bursts
  Fast radio bursts (FRB) probe the electron density of the universe along the
path of propagation, making high redshift FRB sensitive to the helium
reionization epoch. We analyze the signal to noise with which a detection of
the amplitude of reionization can be made, and its redshift, for various cases
of future FRB survey samples, assessing survey characteristics including total
number, redshift distribution, peak redshift, redshift depth, and number above
the reionization redshift, as well as dependence on reionization redshift. We
take into account scatter in the dispersion measure due to an inhomogeneous
intergalactic medium (IGM) and uncertainty in the FRB host and environment
dispersion measure, as well as cosmology. For a future survey with 500 FRB
extending out to $z=5$, and a sudden reionization, the detection of helium
reionization can approach the $5\sigma$ level and the reionization redshift be
determined to $\sigma(z_r)\approx0.24$ in an optimistic scenario, or $2\sigma$
and $\sigma(z_r)\approx0.34$ taking into account further uncertainties on IGM
fraction evolution and redshift uncertainties.
