Sound-Horizon-Agnostic Inference of the Hubble Constant and Neutrino Mass from BAO, CMB Lensing, and Galaxy Weak Lensing and Clustering

We present a sound-horizon-agnostic determination of the Hubble constant, H₀, by combining DESI DR2 baryon acoustic oscillation (BAO) data with the latest cosmic microwave background (CMB) lensing measurements from Planck, ACT, and SPT-3G, the angular size of the CMB acoustic scale, Dark Energy Survey Year-3 (3×2-pt) galaxy weak lensing and clustering correlations, and the Pantheon+ supernova sample. In this analysis, the sound horizon at the drag epoch, rd, is treated as a free parameter, avoiding assumptions about early-Universe physics. By combining uncalibrated comoving distances from BAO and supernovae with constraints on the matter density Ωₘ h² from CMB and galaxy lensing/clustering, we break the rd-H₀ degeneracy and obtain H₀ = 70.0 ± 1.7 km/s/Mpc when the sum of the neutrino masses is fixed at Σm_ν= 0.06 eV. With a conservative prior on the amplitude of primordial fluctuations, Aₛ, we find H₀ = 70.03 ± 0.97 km/s/Mpc and rd = 144.8 ± 1.6 Mpc. Allowing Σm_ν to vary yields H₀ = 75.3+3.3-4.0 km/s/Mpc and Σm_ν= 0.55+0.23-0.37 ($<1.11$ eV) at 68% (95%) CL, and H₀ = 73.9 ± 2.2 km/s/Mpc with Σm_ν= 0.46+0.21-0.25 (=0.46+0.40-0.45 eV) at 68% (95%) CL when a prior on Aₛ is applied. Forecasts for the completed DESI BAO program, combined with Simons-Observatory-like CMB lensing, next-generation 3×2-pt data, and expanded supernova samples predict σ(H₀) 0.67 km/s/Mpc with fixed Σm_ν, and σ(H₀) 1.1 km/s/Mpc with Σm_ν< 0.133 ($<0.263$) eV at 68% (95%) CL when the neutrino mass is varied. As the precision of BAO, CMB lensing, and galaxy lensing/clustering improve, this rd-agnostic framework will provide an independent test of the need for new physics at recombination.