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Physical Review D


The Hubble tension can be addressed by modifying the sound horizon (rs) before recombination, triggering interest in early universe estimates of the Hubble constant, H0, independent of rs. Constraints on H0 from an rs-free analysis of the full shape BOSS galaxy power spectra within Λ CDM were recently reported and used to comment on the viability of physics beyond Λ CDM. Here we demonstrate that rs-free analyses with current data depend on both the model and the priors placed on the cosmological parameters, such that Λ CDM analyses cannot be used as evidence for or against new physics. We find that beyond-Λ CDM models which introduce additional energy density with significant pressure support, such as early dark energy (EDE) or additional neutrino energy density (ΔNeff), lead to rs-free values of H0 which are larger by 3–4 km/s/Mpc. On the other hand, models which only affect the time of recombination, such as a varying electron mass (Δme), produce H0 constraints similar to Λ CDM. Using BOSS data, constraints from light element abundances, cosmic microwave background (CMB) lensing, a CMB-based prior on the primordial scalar amplitude (As), spectral index (ns), and Ωm from the Pantheon + Type Ia supernovae dataset, we find that in Λ CDM, H0 = 64.9 ± 2.2 km/s/Mpc; in EDE, H0 = 68.7(+3)/(−3.9); in ΔNeff, H0 = 68.1(+2.7)/(−3.8); and in Δme, H0 = 64.7(+1.9)/(−2.3). Using a prior on the angular size of the sound horizon at baryon drag from BAO and CMB measurements, these values become in Λ CDM, H0 = 67.9 ± 1.7; in EDE, H0 = 72.2(+2.9)/(−3.8); in ΔNeff, H0 = 71.5(+2.5)/(−3.3); and in Δme, H0 = 68.0 ± 1.7. With current data, none of the models are in significant tension with SH0ES, and consistency tests based on comparing H0 posteriors with and without rs marginalization are inconclusive with respect to the viability of beyond Λ CDM models.


This work is freely available courtesy of the American Physical Society.

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