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

Revealing the cosmic reionisation history with fast radio bursts in the era of Square Kilometre Array