Revealing the cosmic reionisation history with fast radio bursts in the
  era of Square Kilometre Array
  Revealing the cosmic reionisation history is at the frontier of extragalactic
astronomy. The power spectrum of the cosmic microwave background (CMB)
polarisation can be used to constrain the reionisation history. Here we propose
a CMB-independent method using fast radio bursts (FRBs) to directly measure the
ionisation fraction of the intergalactic medium (IGM) as a function of
redshift. FRBs are new astronomical transients with millisecond timescales.
Their dispersion measure (DM$_{\rm IGM}$) is an indicator of the amount of
ionised material in the IGM. Since the differential of DM$_{\rm IGM}$ against
redshift is proportional to the ionisation fraction, our method allows us to
directly measure the reionisation history without any assumption on its
functional shape. As a proof of concept, we constructed mock non-repeating FRB
sources to be detected with the Square Kilometre Array, assuming three
different reionisation histories with the same optical depth of Thomson
scattering. We considered three cases of redshift measurements: (A)
spectroscopic redshift for all mock data, (B) spectroscopic redshift for 10% of
mock data, and (C) redshift estimated from an empirical relation of FRBs
between their time-integrated luminosity and rest-frame intrinsic duration. In
all cases, the reionisation histories are consistently reconstructed from the
mock FRB data using our method. Our results demonstrate the capability of
future FRBs in constraining the reionisation history.
