Future Constraints on Dark Matter with Gravitationally Lensed Fast Radio Bursts Detected by BURSTT

Understanding dark matter is one of the most urgent questions in modern physics. A very interesting candidate is primordial black holes (PBHs; Carr2016). For the mass ranges of $< 10^{-16} M_{\odot}$ and $> 100 M_{\odot}$, PBHs have been ruled out. However, they are still poorly constrained in the mass ranges of $10^{-16} - 100 M_{\odot}$ (Belotsky et al. 2019). Fast radio bursts (FRBs) are millisecond flashes of radio light of unknown origin mostly from outside the Milky Way. Due to their short timescales, gravitationally lensed FRBs, which are yet to be detected, have been proposed as a useful probe for constraining the presence of PBHs in the mass window of $< 100M_{\odot}$ (Mu\~noz et al. 2016). Up to now, the most successful project in finding FRBs has been CHIME. Due to its large field of view (FoV), CHIME is detecting at least 600 FRBs since 2018. However, none of them is confirmed to be gravitationally lensed (Leung et al. 2022). Taiwan plans to build a new telescope, BURSTT dedicated to detecting FRBs. Its survey area will be 25 times greater than CHIME. BURSTT can localize all of these FRBs through very-long-baseline interferometry (VLBI). We estimate the probability to find gravitationally lensed FRBs, based on the scaled redshift distribution from the latest CHIME catalog and the lensing probability function from Mu\~noz et al. (2016). BURSTT-2048 can detect ~ 24 lensed FRBs out of ~ 1,700 FRBs per annum. With BURSTT's ability to detect nanosecond FRBs, we can constrain PBHs to form a part of dark matter down to $10^{-4}M_{\odot}$.