V2.217: Hubble Tension Arbitration — The Framework’s H0 Prediction

Objective

The Hubble tension — Planck CMB gives H0 = 67.4 ± 0.5 while SH0ES distance ladder gives H0 = 73.0 ± 1.0 — is one of the most debated open problems in cosmology. The entanglement framework, which predicts Omega_Lambda = 0.6877 with zero free parameters, can make a sharp prediction for H0 by combining with a single CMB input (Omega_m h^2). This experiment derives and tests that prediction.

Method

Prediction chain

1. Framework (zero parameters): Omega_Lambda = |delta_total|/(6*alpha_total) = 0.6877
2. Flatness: Omega_m = 1 - Omega_Lambda - Omega_r = 0.3122
3. CMB input (one external measurement): Omega_m h^2 = 0.1430 ± 0.0011 (Planck 2018)
4. Derive H0: h^2 = (Omega_m h^2 + Omega_r h^2) / (1 - Omega_Lambda) → H0 = 67.68 ± 0.26 km/s/Mpc

The error bar (±0.26) comes entirely from the CMB measurement uncertainty, not from the framework.

Results

1. The framework’s H0 prediction

H0 = 67.68 ± 0.26 km/s/Mpc

This is remarkably precise — the framework converts the Planck Omega_m h^2 measurement into an H0 prediction with smaller error bars than Planck’s own LCDM fit (±0.54), because the framework fixes Omega_Lambda exactly rather than marginalizing over it.

2. Tension with H0 measurements

Measurement	H0	Error	Tension	Category
Planck 2018	67.36	0.54	0.5σ	Early
DES Y5 + BAO + BBN	67.40	1.20	0.2σ	Early
DESI DR2 BAO + CMB	67.97	0.38	0.6σ	Early
CCHP 2024 (TRGB+JAGB)	69.85	1.75	1.2σ	Late
SH0ES 2022	73.04	1.04	5.0σ	Late
TDCOSMO 2020	74.20	1.60	4.0σ	Late
H0LiCOW 2020	73.30	1.80	3.1σ	Late
Megamasers	73.90	3.00	2.1σ	Late

All 3 early-universe measurements: consistent (<1σ) 4/5 late-universe measurements: in tension (>2σ)

The one exception is CCHP 2024 (TRGB + JAGB calibration), which gives H0 = 69.85 ± 1.75 — consistent with the framework at 1.2σ. This is notable because the CCHP result uses an independent distance ladder (not Cepheids) and finds a lower H0 than SH0ES.

3. What SH0ES requires

SH0ES H0 = 73.04 requires Omega_Lambda = 0.7319, which is 6.4% above the framework prediction. From V2.216, a +6.4% shift requires ~21 extra real scalars or ~11 extra Weyl fermions beyond the SM. This is far outside the allowed BSM window (max 3 scalars or 2 fermions at 2%).

The framework and SH0ES are mutually exclusive. If SH0ES is correct, the framework is falsified. If the framework is correct, the SH0ES H0 value is wrong.

4. Robustness across CMB experiments

CMB Input	Omega_m h^2	Framework H0	vs SH0ES
Planck 2018	0.1430 ± 0.0011	67.68 ± 0.26	5.0σ
ACT DR4 + WMAP	0.1440 ± 0.0030	67.91 ± 0.71	4.1σ
SPT-3G 2018	0.1410 ± 0.0034	67.20 ± 0.81	4.4σ

All three independent CMB experiments yield framework H0 predictions in the range 67.2 - 67.9, all >4σ from SH0ES. The conclusion is robust to the choice of CMB experiment.

5. Derived cosmological parameters

Parameter	Framework	Planck 2018	Tension
H0 (km/s/Mpc)	67.68	67.36 ± 0.54	0.6σ
Omega_m	0.3122	0.3153 ± 0.0073	0.4σ
Omega_Lambda	0.6877	0.6847 ± 0.0073	0.4σ
Omega_b	0.0488	0.0493 ± 0.0006	0.8σ
omega_cdm h^2	0.1206	0.1200 ± 0.0012	0.5σ
Baryon fraction	0.156	0.157 ± 0.003	0.2σ
Age (Gyr)	13.77	13.80 ± 0.02	1.0σ

Every parameter is within 1σ of the Planck LCDM fit. The framework produces a complete, self-consistent cosmology.

6. Falsification window

The framework predicts H0 = 67.68 ± 0.26. At 3σ, any definitive measurement of H0 > 68.5 or H0 < 66.9 would falsify the framework. This is a narrow, sharp prediction.

Interpretation

The framework takes a side

The Hubble tension has two possible resolutions: (a) systematic errors in the distance ladder, or (b) new physics beyond LCDM. The framework predicts LCDM is correct and H0 ~ 67.7, which means:

1. If the tension is resolved by systematics: The framework is vindicated. The CCHP 2024 result (H0 = 69.85 using TRGB+JAGB instead of Cepheids) already hints at this — different calibrators give lower H0.

2. If the tension is resolved by new physics (H0 ~ 73): The framework is falsified. Omega_Lambda = 0.73 requires 6.4% more vacuum energy than the SM provides, which needs >20 new scalar fields — ruled out by V2.216.

Connection to the full framework story

Experiment	Prediction	Status
V2.197	Omega_Lambda = 0.6877	Matches observation (0.4%)
V2.212	S^3 geometry independence	4% correction only
V2.213	Thermal robustness	<0.15% shift
V2.214	DESI w=-1	Framework predicts w=-1 exactly
V2.215	BAO consistency	BAO fits perfectly (chi2/pt = 1.12)
V2.216	BSM constraints	SUSY ruled out, N_gen=3 selected
V2.217	H0 = 67.68 ± 0.26	5σ against SH0ES, <1σ from Planck

The framework now makes predictions for Omega_Lambda, w, H0, the allowed BSM spectrum, and the number of generations — all from the same self-consistency condition with zero free parameters.

Caveats

1. The H0 prediction uses one external input (Omega_m h^2). The framework predicts Omega_Lambda, not H0 directly. The CMB input is needed to convert Omega_Lambda into H0. However, this input is well-measured and model-independent (it comes from the acoustic peak spacing, not from the LCDM fit).

2. The H0 error bar is deceptively small. The ±0.26 comes from Planck’s Omega_m h^2 uncertainty. The framework’s own theoretical uncertainty (from alpha_s, the graviton contribution, etc.) is not included. If we assign a 0.44% theoretical uncertainty to Omega_Lambda (the current SM overshoot), this adds ~0.15 to the H0 error, giving ±0.30 total.

3. Curvature. We assume spatial flatness (Omega_k = 0). Planck constrains |Omega_k| < 0.002, which would add ~0.1 to the H0 uncertainty.

Tests

8/8 tests pass: Omega_m derivation, H0 value, exact vs simple agreement, SH0ES tension (>3σ), Planck consistency (<2σ), SH0ES Omega_Lambda requirement, age of universe, full comparison output.

Files

• src/hubble_analysis.py: H0 prediction, tension analysis, derived quantities
• tests/test_hubble.py: 8 tests (all pass)
• run_experiment.py: 6-part analysis
• results.npy: Saved numerical results