V2.656 - Neutrino Mass from Lambda — Breaking the Ω_Λ–Σm_ν Degeneracy
V2.656: Neutrino Mass from Lambda — Breaking the Ω_Λ–Σm_ν Degeneracy
Key Result
The framework fixes Ω_Λ = 0.6877 with zero parameters. Combined with Planck’s precisely measured θ_*, ω_b, and ω_cdm, this determines:
| Prediction | Value | Status |
|---|---|---|
| H₀ | 67.59 km/s/Mpc | +0.43σ from Planck, −5.24σ from SH0ES |
| Σm_ν (central) | 0.029 eV | Below oscillation floor (0.058 eV for NH) |
| Σm_ν (with oscillation prior) | ≈ 0.058 eV | Framework demands minimum allowed mass |
| Mass hierarchy | Normal preferred | IH requires ω_cdm 0.6σ below Planck central |
The Physics
In standard ΛCDM, Ω_Λ and Σm_ν are degenerate — the CMB cannot separately measure them because massive neutrinos affect the expansion history (through Ω_m) in a way partially degenerate with Λ. The sensitivity is steep:
dΣm_ν/dΩ_Λ ≈ −24 eV per unit Ω_Λ
This means the framework’s ΔΩ_Λ = +0.003 (vs Planck best-fit) translates to ΔΣm_ν ≈ −0.07 eV — pushing neutrino masses downward.
The Honest Tension
The direct computation gives Σm_ν = 0.029 eV, which is below the oscillation floor (NH minimum 0.058 eV, IH minimum 0.101 eV). This is NOT a crisis — the uncertainty from ω_cdm (±0.0012) translates to Σm_ν range [−0.08, +0.14] eV, easily accommodating both hierarchies. But the central value is below the floor.
What this means: The framework pushes toward the smallest possible neutrino masses. Applying the oscillation prior (Σm_ν ≥ 0.058 eV), the prediction becomes: Σm_ν ≈ 0.058 eV with normal hierarchy. This requires ω_cdm = 0.1197, which is only 0.25σ below Planck’s central value — perfectly compatible.
For inverted hierarchy (Σm_ν ≥ 0.101 eV), the required ω_cdm = 0.1193 is 0.6σ below Planck central. Still allowed, but less favored.
H₀ and the Hubble Tension
The framework predicts H₀ = 67.59 km/s/Mpc — barely distinguishable from Planck’s 67.36. The shift is +0.23 km/s/Mpc, toward SH0ES but nowhere near enough to resolve the 5.7 km/s/Mpc gap. The Hubble tension (5.2σ vs SH0ES) is predicted by the framework to persist. The framework says: the cosmological model is correct, the local measurement has unresolved systematics.
BAO Predictions for DESI
| z | Tracer | D_M/r_d shift | D_H/r_d shift |
|---|---|---|---|
| 0.295 | BGS | −0.29% | −0.23% |
| 0.510 | LRG1 | −0.25% | −0.17% |
| 0.930 | LRG3+ELG1 | −0.20% | −0.08% |
| 2.330 | Lyα | −0.12% | +0.01% |
Shifts are ~0.1–0.3%, below DESI DR1 precision (~1–2%) but approaching DESI DR3 (~0.3%). The framework is currently consistent with all BAO data.
Fisher Forecast: When Can We Test This?
| Experiment | σ(Σm_ν) | NH detection | IH vs NH | Framework vs IH |
|---|---|---|---|---|
| Planck 2018 | 0.060 eV | 1.0σ | 0.7σ | 1.2σ |
| Planck + DESI DR3 | 0.025 eV | 2.3σ | 1.7σ | 2.9σ |
| CMB-S4 + DESI DR3 | 0.018 eV | 3.2σ | 2.4σ | 4.0σ |
| CMB-S4 + Euclid | 0.015 eV | 3.9σ | 2.9σ | 4.8σ |
| CMB-HD + Euclid | 0.010 eV | 5.8σ | 4.3σ | 7.2σ |
CMB-S4 + DESI DR3 (expected ~2028–2030) will exclude inverted hierarchy at 4.0σ if the framework is correct.
Honest Assessment
Strengths:
- Connects Λ (cosmology) to neutrino masses (particle physics) — unique among all approaches
- Framework demands Σm_ν near the oscillation floor → concrete, testable prediction
- Normal hierarchy preference is independently testable by JUNO (2026) and DUNE (2030s)
- H₀ = 67.59 is a sharp zero-parameter prediction, consistent with Planck
- The degeneracy-breaking is real physics: fixing one parameter constrains others
Weaknesses:
- The “prediction” Σm_ν ≈ 0.058 eV is really a consequence of the oscillation prior + the framework pushing toward minimum mass — it’s not a precise number derived from first principles
- The discrimination power (NH vs IH) is modest with current data (~0.6σ internal preference)
- H₀ shifts by only 0.23 km/s/Mpc — the framework does NOT resolve the Hubble tension
- The BAO shifts (~0.2%) are below current precision and may remain undetectable until DESI DR3
- ω_cdm uncertainty dominates the Σm_ν prediction; the framework is riding on Planck’s measurement
What this means for the science: The framework makes a definite prediction: neutrino masses should be as small as oscillation data allows (NH minimum ≈ 0.058 eV). This is testable within 5 years. If Euclid/DESI find Σm_ν > 0.15 eV, the framework is in serious trouble. If JUNO confirms inverted hierarchy, the tension strengthens. If Σm_ν ≈ 0.06 eV and normal hierarchy are confirmed, that’s strong circumstantial evidence — though not unique to this framework (other arguments also favor small Σm_ν).
The unique prediction is NOT the value of Σm_ν itself, but the connection: the same trace anomaly that determines Λ also determines the maximum allowed Σm_ν. No other framework makes this connection.