Fast radio bursts (FRBs) are extra-galactic radio transients which, owing to
the observed dispersion of the signal, can be used as cosmological probes. In
this Letter we use high redshift FRBs to constrain the history of hydrogen
reionization and measure the reionization optical depth {tau}. For the first
time, we do so in a model-independent way by using a free-form parameterization
of the reionization history. In a Bayesian analysis we find that 100 localized
FRBs, produced during the first billion years of cosmic history (redshifts
z>5), are required to surpass the measurement by the Planck satellite,
constraining {tau} to an accuracy of 11% (at 68% confidence) and the midpoint
of reionization to 6%, while 1000 FRBs would further tighten these constraints
to 9% and 3% accuracy respectively.
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