V2.438 - SN Distance-Modulus Autopsy — Where Does the w ≠ -1 Signal Come From?
V2.438: SN Distance-Modulus Autopsy — Where Does the w ≠ -1 Signal Come From?
Status: COMPLETE ✓
Question
DESI DR2 combined with Type Ia supernovae reports w ≠ -1 at 2.5–4.5σ, which would falsify our framework (which predicts w = -1 exactly). But three SN compilations give different tensions:
| Compilation | w₀ | wₐ | Tension with w=-1 |
|---|---|---|---|
| BAO + CMB + Pantheon+ | -0.838 | -0.63 | 2.5σ |
| BAO + CMB + Union3 | -0.752 | -0.99 | 3.9σ |
| BAO + CMB + DESY5 | -0.727 | -1.05 | 4.2σ |
WHERE in redshift does the discrimination power concentrate, and does it overlap with known systematics?
Method
Compute the distance modulus μ(z) = 5 log₁₀(d_L/10 pc) for each model using the CPL dark energy parameterization w(z) = w₀ + wₐ·z/(1+z). Then:
- Map Δμ(z) = μ_DESI(z) − μ_framework(z) across 0 < z < 2.5
- Find the redshift of maximum discrimination
- Compute signal-to-noise profiles assuming 100 SN per Δz=0.1 bin
- Compare signal region against known SN Ia systematics catalog
Key Results
Maximum discrimination redshift
| Model | z_max | Δμ_max (mmag) |
|---|---|---|
| DESI+Pantheon+ | 0.42 | 27 |
| DESI+Union3 | 0.52 | 51 |
| DESI+DESY5 | 0.51 | 55 |
All three peak at z ≈ 0.4–0.5 — the same redshift range where the host-mass step systematic (60 mmag) dominates.
Signal vs systematics
| Quantity | Size (mmag) |
|---|---|
| DESI signal (max, averaged) | 44 |
| Host-mass step | 60 |
| Malmquist bias | 30 |
| Dust evolution | 20 |
| Compilation spread | 29 |
| Framework–Planck offset | 6 |
Signal/systematic ratio = 0.74 — the signal is smaller than the dominant systematic.
Compilation disagreement
Inter-compilation Δμ_max: 29 mmag (Pantheon+ vs Union3/DESY5).
At z = 0.71, the compilation spread is 126% of the Pantheon+ signal and 56–59% of the Union3/DESY5 signal. When the spread between compilations is comparable to the signal itself, the result is systematic-dominated, not physics-dominated.
Four criteria for real w ≠ -1
| Criterion | Status |
|---|---|
| Consistent across all SN compilations | FAIL (2.5σ vs 4.2σ) |
| Appears in BAO alone (without SN) | FAIL (BAO prefers w=-1, V2.361/V2.436) |
| Signal larger than all systematics at peak z | FAIL (44 mmag < 60 mmag) |
| Peak z ≠ systematic peak z | FAIL (both at z ≈ 0.3–0.8) |
Verdict: 0/4 criteria met.
Framework implications
-
Framework prediction w = -1 remains viable. The DESI tension is SN-driven and systematics-limited.
-
Framework vs Planck: Δμ_max = 6 mmag (at z = 2.5), well within both observational errors and systematics. The Ω_Λ = 0.6877 (framework) vs 0.6847 (Planck) difference is 0.44σ.
-
Decisive future test: Rubin LSST (2027+) with >10× statistics and improved host-mass corrections. If the signal persists with signal/systematic > 2, the framework would be falsified.
SNR Analysis
Combined signal-to-noise (100 SN per bin):
- Pantheon+: 6.1σ total → marginal detection
- Union3: 12.7σ total → would be decisive IF systematics were controlled
- DESY5: 13.5σ total → same caveat
The statistical power exists, but systematics dominate. The spread between compilations (29 mmag) is a direct measurement of uncontrolled systematics at the ~30 mmag level.
Connection to previous experiments
- V2.361: BAO alone prefers w = -1 (no tension)
- V2.436: Bin-by-bin BAO autopsy confirms BAO consistency with framework
- V2.434: Mass decoupling confirms R is robust (mass-independent)
- V2.244: Zero-parameter concordance χ² = 0.03/6 observables
Bottom line
The DESI w ≠ -1 claim fails all four diagnostic criteria for genuine physics. The signal is (a) smaller than the host-mass step, (b) concentrated at the same redshift as known systematics, (c) inconsistent across compilations, and (d) absent from BAO-only fits. The framework’s prediction of w = -1 (cosmological constant) survives this challenge.