Measuring Hubble constant using localized and unlocalized fast radio bursts

The Hubble constant ($H_0$) is one of the most important parameters in the standard $\rm \Lambda CDM$ model. The measurements given by the main two methods show a gap larger than $4\sigma$, which is known as Hubble tension. Fast radio bursts (FRBs) are extragalactic pulses with durations of milliseconds. They can be used as cosmological probes. We constrain $H_0$ using localized and nonlocalized FRBs. We first used 108 localized FRBs to constrain $H_0$ using the probability distributions of \DMhost and \DMIGM from the IllustrisTNG simulation. Then, we used a Monte Carlo sampling to calculate the pseudo-redshift distributions of 527 nonlocalized FRBs from CHIME observations. The 108 localized FRBs yield a constraint of $H_0=69.40_{-1.97}^{+2.14}$ ${\rm km\ s^{-1} Mpc^{-1}}$, which lies between the early- and late-time values. The constraint of $H_{0}$ from nonlocalized FRBs yields $H_0=68.81_{-0.68}^{+0.68}$ ${\rm km\ s^{-1} Mpc^{-1}}$. This result indicates that the uncertainty on the constraint of $H_0$ drops to $\sim1\%$ when the number of localized FRBs is increased to $\sim500$. These uncertainties only include the statistical error. The systematic errors are also discussed and play a dominant role in the current sample.