Bayesian TRGB Calibration and the Hubble Tension

We present a novel Bayesian hierarchical framework for calibrating the Tip of the Red Giant Branch (TRGB) absolute magnitude using Gaia Data Release 3 (DR3) parallaxes, propagating correlated uncertainties and modelling selection eects self-consistently. Combining this geometric anchor with baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) Year-1 data release and cosmic microwave background (CMB) constraints from Planck 2018, we construct an inverse distance ladder that constrains the Hubble constant, H 0 , with reduced sensitivity to local calibrator systematics. Our hierarchical model explicitly marginalises over the Gaia parallax zero-point, LutzKelker bias, and metallicity-dependent TRGB luminosity variations. Analysing 412 RGB stars in 8 Milky Way globular clusters with precise Gaia DR3 astrometry and ground-based I-band photometry, we derive M TRGB I = −4.025 ± 0.022 (stat) ± 0.028 (sys) mag. Incorporating DESI BAO measurements at z eff = 0.51, 0.71, and 1.49, we obtain H 0 = 69.8 ± 1.3 km s −1 Mpc −1 , intermediate between the Planck CMB inference (67.4 ± 0.5 km s −1 Mpc −1) and local Cepheidbased determinations (73.0 ± 1.0 km s −1 Mpc −1). The tension between our result and the SH0ES measurement is 2.2σ, while agreement with Planck is at 1.7σ. We present extensive systematic checks including parallax zero-point variations, photometric calibration tests, and mock-catalogue injectionrecovery analyses. Our framework provides a template for incorporating future Gaia releases and JWST TRGB measurements, with projected uncertainties of δH 0 < 1.0 km s −1 Mpc −1 achievable by 2028.