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

Ioannis Pantos, Leandros Perivolaropoulos

TL;DR

The paper challenges the conventional Early-vs-Late framing of the Hubble tension by compiling 83 Sound-Horizon-independent $H_0$ measurements and classifying them into four categories that separate Distance Ladder from non-Ladder methods and model dependence. Using inverse-variance weighting and chi-squared diagnostics, it finds $H_0 = 72.74 \pm 0.40$ for Distance Ladder, and $H_0 = 68.67 \pm 0.46$ for the rest, yielding a robust $\sim 6.7\sigma$ tension (4.5$\sigma$ after accounting for correlations). An internal $2.4\sigma$ tension is identified within One-Step measurements: ΛCDM assumptions push $H_0$ downward by about $3.2$ km s$^{-1}$ Mpc$^{-1}$ relative to model-independent analyses, suggesting either unrecognized ladder systematics or genuine deviations from ΛCDM at late times. The results challenge pure Early Dark Energy as a complete fix, highlight the critical role of model assumptions, and indicate that resolving the tension will likely require a combination of improved, model-independent measurements and careful scrutiny of distance-calibrator physics.

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 83 Sound-Horizon-independent $H_0$ measurements, categorized into four classes: Distance Ladder measurements using local calibrators; Local One-Step $Λ$CDM measurements assuming the standard expansion history; Pure Local One-Step measurements independent of $H(z)$ shape; and CMB Sound Horizon free measurements using CMB data without the Sound Horizon scale. We find that the 29 Distance Ladder measurements yield $H_0 = 72.74 \pm 0.40$ km s$^{-1}$ Mpc$^{-1}$ ($χ^2_ν\equiv χ^2/d.o.f= 0.74$), while the 54 One-Step measurements collectively yield $H_0 = 68.67 \pm 0.46$ km s$^{-1}$ Mpc$^{-1}$ ($χ^2_ν= 0.85$), a $6.7σ$ tension exceeding the Planck--SH0ES discrepancy. This tension remains significant at $4.5σ$ after accounting for correlations. Among One-Step categories, Local One-Step $Λ$CDM measurements favor the lowest value ($H_0 = 67.18 \pm 0.90$ km s$^{-1}$ Mpc$^{-1}$), Pure Local One-Step yield an intermediate value ($H_0 = 70.38 \pm 1.00$ km s$^{-1}$ Mpc$^{-1}$), and CMB Sound Horizon Free measurements give $H_0 = 68.71 \pm 0.63$ km s$^{-1}$ Mpc$^{-1}$. Thus, 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 $2.4σ$ internal tension among One-Step measurements: analyses assuming $Λ$CDM systematically recover lower $H_0$ values by about 3.2 km s$^{-1}$ Mpc$^{-1}$ compared to model-independent methods. This suggests either unrecognized systematics/physics in the Distance Ladder or deviations from $Λ$CDM in the late-time Universe.

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

TL;DR

The paper challenges the conventional Early-vs-Late framing of the Hubble tension by compiling 83 Sound-Horizon-independent measurements and classifying them into four categories that separate Distance Ladder from non-Ladder methods and model dependence. Using inverse-variance weighting and chi-squared diagnostics, it finds for Distance Ladder, and for the rest, yielding a robust tension (4.5 after accounting for correlations). An internal tension is identified within One-Step measurements: ΛCDM assumptions push downward by about km s Mpc relative to model-independent analyses, suggesting either unrecognized ladder systematics or genuine deviations from ΛCDM at late times. The results challenge pure Early Dark Energy as a complete fix, highlight the critical role of model assumptions, and indicate that resolving the tension will likely require a combination of improved, model-independent measurements and careful scrutiny of distance-calibrator physics.

Abstract

The Hubble tension is commonly framed as a discrepancy between local, late-time measurements favoring km s Mpc and early-time, Sound-Horizon-based measurements favoring km s Mpc. We challenge this viewpoint by analyzing 83 Sound-Horizon-independent measurements, categorized into four classes: Distance Ladder measurements using local calibrators; Local One-Step CDM measurements assuming the standard expansion history; Pure Local One-Step measurements independent of shape; and CMB Sound Horizon free measurements using CMB data without the Sound Horizon scale. We find that the 29 Distance Ladder measurements yield km s Mpc (), while the 54 One-Step measurements collectively yield km s Mpc (), a tension exceeding the Planck--SH0ES discrepancy. This tension remains significant at after accounting for correlations. Among One-Step categories, Local One-Step CDM measurements favor the lowest value ( km s Mpc), Pure Local One-Step yield an intermediate value ( km s Mpc), and CMB Sound Horizon Free measurements give km s Mpc. Thus, 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 internal tension among One-Step measurements: analyses assuming CDM systematically recover lower values by about 3.2 km s Mpc compared to model-independent methods. This suggests either unrecognized systematics/physics in the Distance Ladder or deviations from CDM in the late-time Universe.
Paper Structure (75 sections, 20 equations, 4 figures, 11 tables)

This paper contains 75 sections, 20 equations, 4 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Data Compilation and Categorization
  3. Selection Criteria
  4. Classification Methodology
  5. Category 1: Distance Ladder Measurements
  6. Category 2: Local One-Step (ΛCDM Assumption)
  7. Category 3: Pure Local One-Step (Model Independent)
  8. Category 4: CMB Sound Horizon Free
  9. Summary of Classification
  10. Statistical Analysis and Results
  11. Methodology
  12. Weighted Mean Statistics by Category
  13. Category 1: Distance Ladder (H0 = 72.74 ± 0.40)
  14. Category 2: Local One-Step ΛCDM (H0 = 67.18 ± 0.90)
  15. Category 3: Pure Local One-Step (H0 = 70.38 ± 1.00)
  16. ...and 60 more sections

Figures (4)

  • Figure 1: Decision tree for classifying H0 measurements into the four categories. Category assignments are based on explicit methodological statements in the original publications.
  • Figure 2: Gaussian probability distributions of the four measurement categories. The visual separation is striking: Category 1 (Distance Ladder, blue peak) is isolated at high $H_0$. Categories 2 (Local One-Step $\Lambda$CDM) and 4 (CMB Sound Horizon Free) overlap significantly at low $H_0$, demonstrating that local data analyzed under $\Lambda$CDM align with early-universe constraints. Category 3 (Pure Local One-Step) occupies a broader, intermediate region, highlighting the shift in central value when $\Lambda$CDM model assumptions are relaxed. The black curve represents the ensemble of all One-Step measurements. The Planck 2018 value ($H_0 = 67.4 \pm 0.5$ km s$^{-1}$ Mpc$^{-1}$) and SH0ES value ($H_0 = 73.04 \pm 1.04$ km s$^{-1}$ Mpc$^{-1}$) are indicated for reference.
  • Figure 3: The blue curve represents Category 1 (Distance Ladder, $H_0 = 72.74 \pm 0.40$ km s$^{-1}$ Mpc$^{-1}$), while the red curve represents the combined ensemble of all Sound-Horizon-independent One-Step measurements (Categories 2+3+4, $H_0 = 68.67 \pm 0.46$ km s$^{-1}$ Mpc$^{-1}$). The weighted mean tension between these two aggregate samples is $6.7\sigma$ (or $4.5\sigma$ after correlation adjustment). The vertical dashed line indicates the Planck 2018 value.
  • Figure 4: Evidence for bimodality in the One-Step distribution. The dashed curve represents the inverse-variance weighted sum of Gaussians incorporating all One-Step measurements (Categories 2, 3, and 4). The solid curve shows the distribution after excluding the two highest-precision Pogosian et al. Pogosian2024 measurements. The latter reveals an underlying bimodal structure with peaks near $H_0 \approx 67$ and $H_0 \approx 73$ km s$^{-1}$ Mpc$^{-1}$, previously concealed by the dominant contribution of the high-weight measurements.