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tokens: et al. 2007 ; Thornton et al. 2013 ; Petroff et al. 2015 , 2016 ). Although the progenitors of these events are debated, the large values of the dispersion measure (DM) in excess of the Galactic value of these events (Dolag et al. 2015 ) suggest they are extragalactic or even cosmological in origin. The localization of the repeating burst FRB 121102 at z ∼ 0.19 has firmly established the cosmological origin of at least this event (Scholz et al. 2016 ; Spitler et al. 2016 ; Chatterjee et al. 2017 ; Marcote et al. 2017 ; Tendulkar et al. 2017 ). The observed DM of an FRB therefore should at least have a significant contribution from the intergalactic medium (IGM). Based on the average DM– z relation, one can estimate that the FRBs are typically at distances of the order of a gigaparsec (Ioka 2003 ; Inoue 2004 ; Deng Zhang 2014 ; Zheng et al. 2014 ; Zhang 2018 ). The cosmological origin of FRBs allows them to become promising tools to study the universe and fundamental physics, e.g., probing baryon density and spatial distribution (Deng Zhang 2014 ; Mcquinn 2014 ), constraining the dark energy equation of state (Gao et al. 2014 ; Zhou et al. 2014 ; Weltman et al. 2018 ), probing the ionization history of the universe (Deng Zhang 2014 ; Zheng et al. 2014 ), tracing the large-scale structure of the universe (Masui Sigurdson 2015 ), testing Einstein’s equivalence principle (Wei et al. 2015 ; Nusser 2016 ; Tingay Kaplan 2016 ), constraining the rest mass of the photon (Wu et al. 2016 ; Shao Zhang 2017 ), measuring the cosmic proper distance (Yu Wang 2017 ), as well as constraining the magnetic fields in the IGM (Akahori et al. 2016 ). Thanks to another two properties of these mysterious transients, i.e., narrow durations (∼(1–10) ms; Lorimer et al. 2007 ; Keane et al. 2011 ; Thornton et al. 2013 ; Spitler et al. 2014 ; Petroff et al. 2015 ; Ravi et al. 2015 ; Champion et al. 2016 ; Petroff et al. 2016 ; Spitler et al. 2016 ) and a high event rate (∼10 3 –10 4 per day all sky; Thornton et al. 2013 ; Champion et al. 2016 ), lensed FRBs have been proposed as a probe of compact dark matter (Muñoz et al. 2016 ; Wang Wang 2018 ), motion of the FRB source (Dai Lu 2017 ), as well as precision cosmology (Li et al. 2018 ). In practice, there are some issues that hinder the application of FRBs for cosmological purposes. First, it is not easy to measure the redshifts of most FRBs. Localizing them is possible if they repeat, but it is possible that only a fraction of FRBs repeat (Palaniswamy et al. 2018 ). Recently, the Canadian Hydrogen Intensity Mapping Experiment (CHIME; using the CHIME/FRB instrument) has reported detections of 13 FRBs during a precommissioning phase (The CHIME/FRB Collaboration 2019a ). It is more exciting that 1 of the 13 FRBs is a second source of repeaters, which suggests that CHIME/FRB and other wide-field sensitive radio telescopes will find a substantial population of repeating FRBs (The CHIME/FRB Collaboration 2019b ). The second