H0 from cosmological energy-density measurements: Big Bang Nucleosynthesis, the BAO amplitude, and the Alcock-Paczynski effect

The Hubble tension has reached >5-σ significance, demanding a change to the ΛCDM model barring unknown systematics in local or CMB measurements. H₀ from the CMB can be increased by decreasing the sound horizon at recombination, for instance by adding extra early dark energy (EDE) at z~1000. Hence, sound horizon free H₀ measurements provide a model-independent test of the Hubble tension. We measure H₀ without the sound horizon by combining Ω_m from the Alcock-Paczynski effect, Ω_bh² from Big Bang Nucleosynthesis calibrated via the primordial helium and deuterium abundance, and Ω_b/Ω_m from the amplitude of the baryon acoustic feature. The first two measurements are well-established in previous work; we validate BAO amplitude measurements using N-body mocks and apply it to BOSS data. We find that two separate approaches are consistent: adding BAO amplitude as an extra parameter to “template-fit” pre- and post-reconstruction BAO models with a damped linear power spectrum; and adding BAO amplitude to the full-shape perturbation theory code CLASS-PT. We explicitly verify that this method is sound-horizon independent by recovering the correct baryon fraction and H₀ using an EDE model as mock data. We measure the baryon fraction to ~15% across all BOSS redshift bins, leading to ~7% measurements of H0 (σ_H0 ~ 5.5) when combining with BBN and the Alcock-Paczynski parameter from voids. DESI Y5 will improve the precision of this measurement by a factor of 3, allowing 4-σ differentiation of local and CMB values of H₀.