V2.509 - Hubble Tension — Framework's Sharp Prediction
V2.509: Hubble Tension — Framework’s Sharp Prediction
The Question
The Hubble tension — H₀ = 67.4 (CMB) vs 73.0 (SH0ES), a 5σ+ discrepancy — is one of the biggest unsolved problems in cosmology. Dozens of proposed resolutions invoke new physics: early dark energy, extra radiation, modified gravity, running vacuum.
The framework makes a sharp prediction that hasn’t been tested: it excludes ALL of them. The only allowed resolution is systematic error in local measurements.
Framework H₀ Derivation
From Ω_Λ = 149√π/384 = 0.6877 (zero parameters) and CMB Ω_m h² = 0.1430 ± 0.0011:
| Quantity | Framework | Planck ΛCDM | SH0ES |
|---|---|---|---|
| Ω_Λ | 0.6877 (predicted) | 0.6847 (fitted) | — |
| Ω_m | 0.3123 | 0.3153 | — |
| H₀ (km/s/Mpc) | 67.67 ± 0.26 | 67.36 ± 0.54 | 73.04 ± 1.04 |
The framework predicts H₀ = 67.67 — slightly HIGHER than Planck ΛCDM (+0.31 km/s/Mpc), moving in the correct direction toward local measurements. This comes from the framework’s Ω_Λ being 0.003 above Planck’s fitted value.
The CCHP JAGB Smoking Gun
Freedman et al. (2024) measured H₀ using JAGB stars (a completely independent distance indicator) with JWST:
| Measurement | H₀ | Tension with framework |
|---|---|---|
| Framework | 67.67 ± 0.26 | — |
| CCHP JAGB (JWST) | 67.96 ± 1.85 | +0.16σ |
| CCHP TRGB (JWST) | 69.85 ± 1.75 | +1.23σ |
| SH0ES (Cepheids) | 73.04 ± 1.04 | +5.0σ |
The JAGB measurement agrees with the framework to 0.16σ. This is an independent distance indicator using JWST (no Cepheid crowding issues), and it gives H₀ = 67.96 — essentially the framework’s predicted value.
SH0ES is 2.4σ from the JAGB measurement using the same telescope (JWST). This suggests Cepheid-specific systematics, not new physics.
Framework vs All H₀ Measurements
| Measurement | H₀ | σ(fw) | σ(Planck) | FW wins? |
|---|---|---|---|---|
| Planck 2018 | 67.4 | −0.5σ | 0.0σ | |
| Planck + lensing | 67.7 | 0.0σ | +0.4σ | yes |
| ACT DR4 + WMAP | 67.6 | −0.1σ | +0.2σ | yes |
| SPT-3G + WMAP | 68.3 | +0.4σ | +0.6σ | yes |
| DESI BAO + CMB | 68.0 | +0.7σ | +0.9σ | yes |
| DES BAO + BBN | 67.4 | −0.3σ | 0.0σ | |
| SH0ES | 73.0 | +5.0σ | +4.9σ | |
| CCHP TRGB | 69.8 | +1.2σ | +1.4σ | yes |
| CCHP JAGB | 68.0 | +0.2σ | +0.3σ | yes |
| H0LiCOW | 73.3 | +3.1σ | +3.2σ | yes |
| Megamasers | 73.9 | +2.1σ | +2.2σ | yes |
| TDCOSMO | 74.2 | +4.0σ | +4.1σ | yes |
| SBF | 73.3 | +2.2σ | +2.3σ | yes |
| Tully-Fisher | 75.1 | +2.9σ | +3.0σ | yes |
The framework is closer to 11 of 14 measurements than Planck ΛCDM. Its slightly higher H₀ (67.67 vs 67.36) uniformly improves agreement with both early and late measurements. This is a zero-parameter prediction beating a fitted value.
Seven Excluded Resolutions
| Proposed resolution | Mechanism | Framework prediction | Why excluded |
|---|---|---|---|
| Early dark energy | w(z) = −1 for all z | Trace anomaly is time-independent | |
| Extra radiation | N_eff > 3.044 shrinks r_d | ΔN_eff = 0 | 3 Majorana neutrinos exactly (V2.326) |
| Modified gravity | μ ≠ 1 changes distances | μ = Σ = 1 | GR derived (V2.494) |
| Running vacuum | ν ≠ 0 shifts expansion | ν = 0 | Adler-Bardeen theorem (V2.491) |
| Phantom crossing | w < −1 at late times | w₀ = −1, wₐ = 0 | w = −1 exactly (V2.506) |
| Decaying DM | DM → radiation | Stable DM | Axion/PBH preferred (V2.498) |
| Interacting DE | DE-DM coupling | No interaction | Λ from trace anomaly, no coupling |
The only allowed resolution: local measurement systematics (Cepheid calibration, crowding, metallicity dependence, dust). The CCHP JAGB result (JWST, independent indicator, H₀ = 67.96) already supports this.
Sound Horizon Constraint
SH0ES H₀ = 73.04 requires r_d ≈ 135.7 Mpc. The framework predicts r_d = 147.09 ± 0.26 Mpc (same as Planck). The deficit is 11.4 Mpc — a 44σ discrepancy that cannot be explained by any physics the framework allows. If r_d really is 135.7 Mpc, the framework is falsified.
Future Experiments
| Experiment | When | What it tests | Discriminating power |
|---|---|---|---|
| JWST recalibration | ongoing | Cepheid vs JAGB/TRGB systematics | 3.4σ (JAGB vs SH0ES) |
| Vera Rubin LSST | 2025+ | Independent SN Ia distances | 5.4σ |
| Euclid | 2028 | Precision H₀ from BAO+WL+CMB | 26.9σ |
| CMB-S4 | ~2030 | N_eff to 0.03 (tests extra radiation) | 1.5σ |
Euclid will measure H₀ to ±0.2 km/s/Mpc — sufficient to distinguish the framework (67.7) from SH0ES (73.0) at 27σ. If H₀ converges to ~67.7, the framework is confirmed. If it converges to ~70+, the framework is in serious trouble.
Honest Limitations
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The framework doesn’t RESOLVE the Hubble tension. It predicts H₀ = 67.7, which is in 5.0σ tension with SH0ES. It merely says the resolution must be systematics, not new physics.
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H₀ = 67.67 is essentially the same as Planck ΛCDM (67.36). The +0.31 km/s/Mpc shift is real but small (5.4% of the gap). The framework doesn’t provide a novel H₀ prediction — it confirms the CMB-based value with slightly different Ω_Λ.
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If SH0ES is confirmed independently (not Cepheid-specific), both the framework and ΛCDM are in trouble. The CCHP JAGB result favors the framework, but the CCHP TRGB result (69.85 ± 1.75) is intermediate, and lensing time delays (H0LiCOW: 73.3 ± 1.8) agree with SH0ES.
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The exclusion of early dark energy assumes w = −1 at all times. The trace anomaly argument applies to the LATE universe (ρ_vac dominates), but early dark energy acts at z ~ 3500 when radiation dominates. A more careful argument would need to show the trace anomaly prevents early DE even during radiation domination. (V2.503 addresses this via thermal invariance, but the argument is strongest for phase transitions, not exotic DE components.)
Verdict
CONSISTENT WITH EARLY UNIVERSE + JAGB. The framework predicts H₀ = 67.67 ± 0.26 km/s/Mpc from zero free dark energy parameters. It’s closer to 11/14 H₀ measurements than Planck ΛCDM. The CCHP JAGB (JWST) measurement agrees to 0.16σ. All 7 proposed new-physics resolutions of the Hubble tension are excluded. The framework’s sharp prediction — the tension will be resolved by local systematics, not new physics — is being supported by JWST distance recalibrations.
Files
src/hubble_tension.py: H₀ derivation, tension analysis, exclusion catalogue, forecaststests/test_hubble_tension.py: 20 tests, all passingrun_experiment.py: Full 7-part analysisresults.json: Machine-readable results