Dissecting the Hubble tension: Insights from a diverse set of Sound Horizon-free H0 measurements

Abstract

The Hubble tension is commonly framed as a discrepancy between local, late-time measurements favoring $H_0 \approx 73$ km s$^{-1}$ Mpc$^{-1}$ and early-time, Sound-Horizon-based measurements favoring $H_0 \approx 67$ km s$^{-1}$ Mpc$^{-1}$. We challenge this viewpoint by analyzing 88 Sound Horizon Free $H_0$ measurements, categorized into four classes: Distance Ladder measurements using local calibrators; Local $\Lambda$CDM measurements assuming the standard expansion history; Pure Local measurements independent of $H(z)$ shape; and CMB Sound--Horizon--Free measurements using CMB data without the Sound Horizon scale. Our analysis reveals that the 30 Distance Ladder measurements yield $H_0 = 72.73 \pm 0.39$ km s$^{-1}$ Mpc$^{-1}$ ($\chi^2_\nu = 0.72$), while the 58 Distance Ladder-Independent/Sound Horizon Free measurements collectively yield $H_0 = 69.37 \pm 0.34$ km s$^{-1}$ Mpc$^{-1}$ ($\chi^2_\nu = 0.95$), a $6.5\sigma$ tension exceeding the Planck--SH0ES discrepancy. This tension remains significant at a minimum value of $3.9\sigma$ after accounting for correlations. Among categories, Local $\Lambda$CDM measurements favor the lowest value ($H_0 = 67.61\pm 0.96$ km s$^{-1}$ Mpc$^{-1}$), Pure Local yield an intermediate value ($H_0 = 71.03 \pm 0.69$ km s$^{-1}$ Mpc$^{-1}$), and CMB Sound Horizon Free measurements give $H_0 = 69.07 \pm 0.44$ km s$^{-1}$ Mpc$^{-1}$. We conclude that the Hubble tension is better characterized as a discrepancy between the Distance Ladder and all other methodologies, rather than an early-vs-late-time split. We also identify a $2.9\sigma$ internal tension among Distance Ladder Independent/Sound Horizon Free measurements: analyses assuming $\Lambda$CDM systematically recover lower $H_0$ values compared to cosmological-model-independent methods. This suggests either unrecognized systematics in the Distance Ladder or deviations from $\Lambda$CDM or both.