Newest measurements of Hubble constant from DESI 2024 BAO observations

Abstract: In this Letter, we use the latest results from the Dark Energy Spectroscopic Instrument (DESI) survey to measure the Hubble constant. Baryon acoustic oscillation (BAO) observations released by the DESI survey, allow us to determine $H_0$ from the first principles. Our method is purely data-driven and relies on unanchored luminosity distances reconstructed from SN Ia data and $H(z)$ reconstruction from cosmic chronometers. Thus it circumvents calibrations related to the value of the sound horizon size at the baryon drag epoch or intrinsic luminosity of SN Ia. We find $H_0=68.4^{+1.0}_{-0.8}~{\rm km~s^{-1}~Mpc^{-1}}$ at 68% C.L., which provides the Hubble constant at an accuracy of 1.3% with minimal assumptions. Our assessments of this fundamental cosmological quantity using the BAO data spanning the redshift range $z=0.51-2.33$ agree very well with Planck's results and TRGB results within $1\sigma$. This result is still in a $4.3\sigma$ tension with the results of the Supernova H0 for the Equation of State (SH0ES).