V2.537 - Dark Energy Equation of State — Framework w=-1 vs DESI w₀wₐ
V2.537: Dark Energy Equation of State — Framework w=-1 vs DESI w₀wₐ
Status: ALIVE — framework survives at 3.9σ (threshold: 5σ)
Key Result
The framework predicts w = -1 exactly as a theorem (Adler-Bardeen), not an assumption. DESI DR1 reports 2.5-3.9σ hints of w ≠ -1. The framework is under pressure but not yet falsified.
This is the framework’s sharpest falsification target: it makes a zero-parameter prediction (w = -1.0000) that DESI Y5 could confirm or destroy at 8-16σ.
The Derivation: w = -1 from Adler-Bardeen
- δ = one-loop trace anomaly coefficient (-149/12)
- Adler-Bardeen theorem: δ receives no higher-loop corrections
- δ is temperature-independent
- α is UV-dominated (mass corrections < 10⁻³⁴)
- N_eff counts field DOF (temperature-independent)
- R = |δ|/(6α·N_eff) is strictly constant
- Λ = |δ|/(2α·L_H²) is strictly constant
- Constant Λ ⟹ w = p/ρ = -1 exactly
Uncertainty: 0 (this is a theorem, not a measurement).
BAO Confrontation (DESI DR1)
| Model | χ² | k | dof | χ²/dof | AIC | ΔAIC | BIC | ΔBIC |
|---|---|---|---|---|---|---|---|---|
| Framework | 27.8 | 0 | 13 | 2.14 | 27.8 | +3.1 | 27.8 | +1.4 |
| ΛCDM | 28.2 | 1 | 12 | 2.35 | 30.2 | +5.5 | 30.7 | +4.3 |
| w₀wₐ (Pantheon+) | 19.8 | 3 | 10 | 1.98 | 25.8 | +1.1 | 27.5 | +1.1 |
| w₀wₐ (Union3) | 21.2 | 3 | 10 | 2.12 | 27.2 | +2.4 | 28.9 | +2.4 |
| w₀wₐ (DESY5) | 18.7 | 3 | 10 | 1.87 | 24.7 | 0.0 | 26.4 | 0.0 |
Key findings:
- Framework beats ΛCDM on AIC by 2.4 and BIC by 2.9 (fewer parameters compensate for slightly worse χ²)
- w₀wₐ models beat framework by ΔAIC = 1-3 (modest preference for dynamical DE)
- The BAO data alone does not strongly discriminate between models
- χ²/dof ~ 2 for all models suggests unmodeled correlations or systematic effects
DESI Tension with w = -1
| Dataset | w₀ | wₐ | Δw₀/σ | Δwₐ/σ | Combined | Reported |
|---|---|---|---|---|---|---|
| DESI+CMB+Pantheon+ | -0.827 | -0.75 | +2.75 | -2.59 | 3.8σ | 2.5σ |
| DESI+CMB+Union3 | -0.650 | -1.27 | +3.50 | -2.44 | 4.3σ | 3.9σ |
| DESI+CMB+DESY5 | -0.752 | -0.98 | +3.59 | -3.06 | 4.7σ | 3.5σ |
The reported significances (2.5-3.9σ) account for correlations between w₀ and wₐ that our simple quadrature overestimates. Either way: tension exists but is below 5σ.
Framework vs ΛCDM: The Critical Distinction
Both predict w = -1. But:
| ΛCDM | Framework | |
|---|---|---|
| w = -1 | Assumption | Theorem (Adler-Bardeen) |
| Ω_Λ | Free parameter (fit to CMB) | Predicted: R = 0.6877 |
| If w ≠ -1 confirmed | Replace with new DE model | Falsified |
| Fine-tuning | 120 digits | 0 digits |
w(z) Evolution
| z | Framework | Pantheon+ | Union3 | DESY5 |
|---|---|---|---|---|
| 0.0 | -1.0000 | -0.8270 | -0.6500 | -0.7520 |
| 0.5 | -1.0000 | -1.0770 | -1.0733 | -1.0787 |
| 1.0 | -1.0000 | -1.2020 | -1.2850 | -1.2420 |
| 2.0 | -1.0000 | -1.3270 | -1.4967 | -1.4053 |
Framework: flat line at w = -1. DESI w₀wₐ: w crosses -1 near z ≈ 0.3 and evolves away.
Future Projections
DESI Y5 (expected 2026-2027):
- Projected σ(w₀) = 0.03, σ(wₐ) = 0.12
- If Pantheon+-like best-fit holds: 8.5σ tension → framework falsified
- If Union3-like best-fit holds: 15.8σ tension → framework falsified
- If DESY5-like best-fit holds: 11.6σ tension → framework falsified
Euclid (2027+):
- Projected σ(Ω_Λ) = 0.002
- Framework prediction: 0.6877 vs Planck 0.6847 → 1.5σ tension
Falsification Scorecard
| Test | Status | Current Tension | Threshold |
|---|---|---|---|
| w = -1 (Adler-Bardeen) | ALIVE | 2.5-3.9σ | 5σ |
| Ω_Λ = 0.6877 | ALIVE | +0.4σ | 5σ |
| No new gauge bosons | ALIVE | no discoveries | any detection |
| Constant Λ (no epoch variation) | ALIVE | consistent | any variation |
Honesty Notes
- The χ²/dof ~ 2 for all models suggests our simple diagonal-covariance BAO fit is missing correlations between DM and DH at the same z_eff. A proper analysis would use the full DESI covariance matrix.
- The framework’s survival depends on DESI’s w ≠ -1 signal being a statistical fluctuation or systematic artifact. This is a genuine open question.
- If DESI Y5 confirms the current best-fit at the projected precision, the framework is falsified at >8σ with no escape route (Adler-Bardeen admits no free parameters).
- The framework makes the sharpest possible prediction (w = -1.0000, zero uncertainty) which is both its greatest strength and its greatest vulnerability.
Tests
37/37 passed covering: framework predictions, cosmological distances, BAO χ², Adler-Bardeen chain, DESI tension analysis, future projections, model comparison.