V2.639 - Hubble Tension Anatomy — H₀ Diagnosis Within the Framework
V2.639: Hubble Tension Anatomy — H₀ Diagnosis Within the Framework
Question
The framework fixes Ω_Λ = 0.6877 (slightly above Planck’s 0.6847). Does this shift H₀ in the right direction? Can the framework say anything about the 5.7σ Hubble tension between CMB (67.4 km/s/Mpc) and SH0ES (73.0 ± 1.0 km/s/Mpc)?
Method
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CMB route: Given Ω_Λ and CMB-measured physical densities (ω_m = 0.1424, ω_r), solve for H₀ via the acoustic scale θ* = r_s / D_C(z*). Iterate since Ω_m = ω_m/h² depends on H₀.
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BAO inverse distance ladder: From each DESI DR1 D_H/r_d and D_M/r_d measurement, infer H₀ assuming the framework’s Ω_Λ and Planck’s r_d.
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Sensitivity analysis: Scan Ω_Λ from 0.60 to 0.85 to determine dH₀/dΩ_Λ and what Ω_Λ would be needed to match SH0ES.
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BAO predictions: Compute framework predictions for all 13 DESI DR1 distance measurements and assess χ².
Results
1. Framework H₀ prediction
| Parameter | Framework | Planck |
|---|---|---|
| Ω_Λ | 0.6877 | 0.6847 |
| Ω_m | 0.3157 | 0.3171 |
| H₀ | 67.15 | 67.01 |
ΔH₀ = +0.14 km/s/Mpc — 2.5% of the 5.7 km/s/Mpc SH0ES gap.
The framework’s higher Ω_Λ pushes H₀ in the right direction but the shift is utterly negligible. The Hubble tension is 5.7σ within the framework.
2. Sensitivity dH₀/dΩ_Λ
dH₀/dΩ_Λ = 46.9 km/s/Mpc per unit Ω_Λ.
To match SH0ES: Ω_Λ = 0.813, requiring Ω_m = 0.187. This is impossible within the framework (would require removing most of the SM field content) and is ruled out by CMB, BAO, and SNe independently.
3. BAO inverse distance ladder
| Route | H₀ (km/s/Mpc) |
|---|---|
| CMB θ* | 67.15 |
| BAO D_H/r_d | 68.40 ± 0.71 |
| BAO D_M/r_d | 68.05 ± 0.53 |
| BAO combined | 68.18 ± 0.42 |
| SH0ES (local) | 73.04 ± 1.04 |
| TRGB (local) | 69.8 ± 1.7 |
Internal consistency: D_H vs D_M routes agree to 0.4σ. CMB vs BAO show 2.4σ tension, driven by the z=0.510 LRG1 D_H bin (+3.0σ pull) — the same bin that drives DESI’s w₀-wₐ dark energy preference.
4. Framework BAO predictions vs DESI DR1
| z | Type | DESI | Framework | Pull |
|---|---|---|---|---|
| 0.295 | D_V | 7.93 ± 0.15 | 8.09 | +1.0σ |
| 0.510 | D_M | 13.62 ± 0.25 | 13.55 | −0.3σ |
| 0.510 | D_H | 20.98 ± 0.61 | 22.83 | +3.0σ |
| 0.706 | D_M | 16.85 ± 0.32 | 17.77 | +2.9σ |
| 0.706 | D_H | 20.08 ± 0.61 | 20.25 | +0.3σ |
| 0.930 | D_M | 21.71 ± 0.28 | 22.01 | +1.1σ |
| 0.930 | D_H | 17.88 ± 0.35 | 17.68 | −0.6σ |
| 1.317 | D_M | 27.79 ± 0.69 | 28.13 | +0.5σ |
| 1.317 | D_H | 13.82 ± 0.42 | 14.15 | +0.8σ |
| 1.491 | D_M | 30.69 ± 0.80 | 30.48 | −0.3σ |
| 1.491 | D_H | 13.23 ± 0.47 | 12.88 | −0.7σ |
| 2.330 | D_M | 39.71 ± 0.94 | 39.33 | −0.4σ |
| 2.330 | D_H | 8.52 ± 0.17 | 8.65 | +0.7σ |
χ²/dof = 22.3/13 = 1.72 (p = 0.051) — marginal. The tension is driven by two bins: z=0.510 D_H (+3.0σ) and z=0.706 D_M (+2.9σ). These are the same LRG bins that drive DESI’s evolving dark energy preference.
5. Can ANY Ω_Λ resolve the Hubble tension?
| Ω_Λ | H₀ (km/s/Mpc) | SH0ES gap |
|---|---|---|
| 0.60 | 63.4 | +9.6 |
| 0.65 | 65.5 | +7.6 |
| 0.70 | 67.7 | +5.3 |
| 0.75 | 70.4 | +2.7 |
| 0.80 | 73.4 | −0.4 |
| 0.85 | 77.0 | −4.0 |
Matching SH0ES requires Ω_Λ ≈ 0.80 → Ω_m ≈ 0.20, which is excluded at >10σ by CMB, BAO, galaxy clustering, and weak lensing.
Key Findings
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H₀ shift is negligible: ΔH₀ = +0.14 km/s/Mpc, 2.5% of the SH0ES gap. The Hubble tension is 5.7σ within the framework — same as Planck ΛCDM.
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The Hubble tension is NOT a cosmological constant problem. Even scanning Ω_Λ to 0.80 (far beyond any physical model), H₀ only reaches 73.4. The tension is orthogonal to the dark energy sector.
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The H₀ tension must come from pre-recombination physics (modified r_s via early dark energy, extra radiation, non-standard recombination) or from systematics in the local distance ladder. Neither affects the framework’s Ω_Λ prediction.
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BAO marginal tension (p=0.051) is localised to two LRG bins (z=0.51, 0.71) — the same bins driving DESI’s w₀-wₐ preference. This is a data feature, not a framework failure.
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Framework is insulated from the H₀ tension. Whatever resolves the tension changes r_s or the calibration ladder, not Ω_Λ. The framework’s prediction is robust to the H₀ resolution.
Significance
This experiment closes a gap in the framework’s observational confrontation. Previous experiments tested Ω_Λ against BAO distances (V2.607), growth rate (V2.636), and SNe (V2.570). This experiment addresses the complementary question: what does the framework say about H₀?
Answer: almost nothing, and that’s the right answer. The cosmological constant and the Hubble tension are different problems with different solutions. The framework solves the first (deriving Ω_Λ from field content) without needing to touch the second (which requires pre-recombination or distance-ladder physics).
Technical Notes
- H₀ from θ* computed iteratively (30 iterations, convergence to 0.001 km/s/Mpc)
- Physical densities from Planck 2018 TT,TE,EE+lowE+lensing (Table 2)
- DESI DR1 BAO data from arXiv:2404.03002 (Table 1)
- Sound horizon r_d = 147.09 Mpc, r_s = 144.43 Mpc (Planck 2018)
- Radiation density includes 3 massless neutrino species (N_eff = 3.044)
- BAO inverse distance ladder assumes Planck r_d calibration