Dispersion Measure Distribution of Unlocalized Fast Radio Bursts as a Probe of the Hubble Constant

We present constraints on the Hubble constant ($H_0$) derived from the observed dispersion measure (DM) distribution of unlocalized fast radio bursts (FRBs). While localized FRBs with redshift measurements have been used to investigate the Hubble tension, their sample remains limited. Here we demonstrate that unlocalized FRBs -- which are far more numerous -- can independently constrain $H_0$ without requiring redshift information, as cosmic expansion imprints itself on their DM distribution. Analyzing a selected sample of 2124 unlocalized FRBs from the CHIME Catalog II, we obtain $H_0 = 73.8^{+14.0}_{-12.3}~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ at the $1\sigma$ confidence level, corresponding to an uncertainty of about 18%. Breaking the degeneracy between $H_0$ and the characteristic cutoff energy $E_*$ of the FRB isotropic energy distribution would reduce this uncertainty to 9%. This work constitutes the first $H_0$ measurement derived solely from the DM distribution of unlocalized FRBs, highlighting their potential as a new cosmological probe. Future joint analyses with localized FRBs promise even tighter constraints.