A measurement of Hubble's Constant using Fast Radio Bursts

We constrain the Hubble constant H$_0$ using Fast Radio Burst (FRB) observations from the Australian Square Kilometre Array Pathfinder (ASKAP) and Murriyang (Parkes) radio telescopes. We use the redshift-dispersion measure (`Macquart') relationship, accounting for the intrinsic luminosity function, cosmological gas distribution, population evolution, host galaxy contributions to the dispersion measure (DM$_{\rm host}$), and observational biases due to burst duration and telescope beamshape. Using an updated sample of 16 ASKAP FRBs detected by the Commensal Real-time ASKAP Fast Transients (CRAFT) Survey and localised to their host galaxies, and 60 unlocalised FRBs from Parkes and ASKAP, our best-fitting value of H$_0$ is calculated to be $73_{-8}^{+12}$ km s$^{-1}$ Mpc$^{-1}$. Uncertainties in FRB energetics and DM$_{\rm host}$ produce larger uncertainties in the inferred value of H$_0$ compared to previous FRB-based estimates. Using a prior on H$_0$ covering the 67--74 km s$^{-1}$ Mpc$^{-1}$ range, we estimate a median DM$_{\rm host} = 186_{-48}^{+59}$ km s$^{-1}$ Mpc$^{-1}$, exceeding previous estimates. We confirm that the FRB population evolves with redshift similarly to the star-formation rate. We use a Schechter luminosity function to constrain the maximum FRB energy to be $\log_{10} E_{\rm max}=41.26_{-0.22}^{+0.27}$ erg assuming a characteristic FRB emission bandwidth of 1 GHz at 1.3 GHz, and the cumulative luminosity index to be $\gamma=-0.95_{-0.15}^{+0.18}$. We demonstrate with a sample of 100 mock FRBs that H$_0$ can be measured with an uncertainty of $\pm 2.5$ km s$^{-1}$ Mpc$^{-1}$, demonstrating the potential for clarifying the Hubble tension with an upgraded ASKAP FRB search system. Last, we explore a range of sample and selection biases that affect FRB analyses.