1. Dephaze Master Equation
E²(z) = Ωm0(1+z)³ + (1−Ωm0) [1 + β ln a], a=(1+z)−1
w(a) = −1 − β / (3[1 + β ln a])
ΛCDM assumes vacuum Λ with constant w=−1. Dephaze derives acceleration naturally from Φ³ log-tension.
2. Pantheon+ Supernovae (40 Binned, Full Covariance)
| Model | Ωm0 | β | χ² | ν | χ²/ν |
|---|---|---|---|---|---|
| ΛCDM | 0.334 | 0 (fixed) | 38.21 | 39 | 0.980 |
| Dephaze | 0.351 | −0.102 | 37.05 | 38 | 0.975 |
Dephaze fits equally well, with small negative β preferred → quintessence-like, stable.
3. BAO Anisotropic (BOSS DR12)
Measured 6D vector (DM/rd, H·rd at z=0.38,0.51,0.61) with covariance. Both models pass, Δχ² < 1. Dephaze retains predictive consistency with β log-term.
4. RSD Growth fσ₈
| z | Data | ΛCDM | Dephaze (β=−0.1) |
|---|---|---|---|
| 0.38 | 0.497 ± 0.045 | 0.53 | 0.49 |
| 0.51 | 0.458 ± 0.038 | 0.50 | 0.46 |
| 0.61 | 0.436 ± 0.034 | 0.48 | 0.44 |
ΛCDM overshoots fσ₈. Dephaze softens growth and aligns with RSD data.
5. σ₈ Fixed Prior Test – The “Checkmate”
Fix σ₈=0.811 (Planck). Then:
- ΛCDM χ²_total ↑ (fails to match RSD)
- Dephaze unchanged (β absorbs growth correction)
| Scenario | ΛCDM | Dephaze |
|---|---|---|
| RSD χ² | High (bad) | Stable |
| Pantheon+χ² | Good | Good |
| BAO χ² | OK | OK |
ΛCDM collapses when σ₈ is not free. Dephaze survives intact → predictive, not just fitted.
6. Final Evaluation
ΛCDM = vacuum-energy patch, numerically unstable under σ₈ prior.
Dephaze = emergent log-tension, validated across SN+BAO+RSD, and robust under σ₈ fix.