V2.527: Neutrino Mass Prediction from Lambda

Motivation

The framework predicts Ω_Λ = 149√π/384 = 0.6877 with zero free parameters. In ΛCDM, Σm_ν and Ω_Λ are degenerate in CMB data — increasing neutrino mass can be partially compensated by decreasing Ω_Λ. The framework breaks this degeneracy by fixing Ω_Λ, yielding a tighter constraint on neutrino mass.

Combined with oscillation data (NuFIT 5.3), this produces a complete prediction for the neutrino mass spectrum — something ΛCDM cannot do.

Method

1. Compute mass eigenvalues from oscillation data (Δm²₂₁, Δm²₃₁) as functions of the lightest mass m_lightest, for both normal (NH) and inverted (IH) hierarchies.

2. Derive the framework’s upper bound on Σm_ν by breaking the Σm_ν−Ω_Λ degeneracy. With Ω_Λ fixed, ~40% of the Planck Σm_ν uncertainty is removed, tightening the 95% CL bound from 120 meV to ~93 meV.

3. Determine hierarchy preference: IH minimum (99 meV) exceeds the framework bound (93 meV) → IH excluded at 95% CL.

4. Compute the allowed mass range for NH, cosmological parameters (H₀, age), and effective Majorana mass m_ββ.

Key Results

1. Framework Predicts Normal Hierarchy

Hierarchy	Minimum Σm_ν	Framework bound (95% CL)	Status
Normal	59 meV	93 meV	ALLOWED
Inverted	99 meV	93 meV	EXCLUDED

IH is excluded because its minimum Σm_ν (99 meV) exceeds the framework’s upper bound (93 meV). The margin is only 6 meV — a firm but not overwhelming exclusion.

2. Predicted Mass Spectrum (NH)

Quantity	Value	Unit
m₁ (lightest)	[0, 19]	meV
m₂	[8.6, 20.6]	meV
m₃ (heaviest)	[50.1, 53.5]	meV
Σm_ν	[59, 93]	meV
m_ββ (Majorana)	[3.7, 20]	meV

The degeneracy-breaking analysis (Phase 9) shows the framework’s best-fit is at the NH floor: Σm_ν ≈ 59 meV, m₁ ≈ 0.

3. Cosmological Parameters

At Σm_ν = 59 meV (NH minimum):

• H₀ = 67.68 km/s/Mpc
• Ω_m = 0.3123
• Age = 13.773 Gyr

These shift by <0.5% across the allowed Σm_ν range.

4. Experimental Tests

Experiment	Observable	Sensitivity	Year	Framework prediction
JUNO	Hierarchy	3σ NH vs IH	2027	NH
DESI Y5 + CMB	Σm_ν	< 40 meV (95%)	2028	59 meV (detection)
CMB-S4 + DESI	Σm_ν	< 20 meV (95%)	2030	59 meV (2.9σ detection)
LEGEND-1000	m_ββ	< 15 meV	2030	3.7 meV (below reach)
nEXO	m_ββ	< 7 meV	2032	3.7 meV (below reach)

5. Kill Conditions

1. IH confirmed by JUNO → framework falsified
2. Σm_ν > 93 meV detected → exceeds framework bound
3. Dirac neutrinos confirmed → framework requires Majorana (V2.326)
4. 4th neutrino species (N_eff > 3.1) → breaks Ω_Λ prediction

What This Means

The framework extends its predictive reach from cosmology into particle physics. From a single formula (Ω_Λ = 149√π/384), combined with neutrino oscillation data, it predicts:

• Normal hierarchy (IH excluded at 95% CL)
• Σm_ν ≈ 59 meV (at the oscillation minimum, m₁ ≈ 0)
• Majorana neutrinos (from V2.326)
• m_ββ ≈ 3.7 meV (below next-generation 0νββ experiments)

These predictions are testable by 2030. ΛCDM makes none of them.

Caveats

1. The 40% degeneracy fraction is an estimate. A full MCMC with Planck likelihoods would give a more precise bound. The IH exclusion margin (6 meV) is narrow enough that this matters.

2. The framework assumes 3 Majorana neutrinos (from V2.326). If this assumption is wrong, the mass predictions change.

3. The Σm_ν−Ω_Λ degeneracy slope (−8 eV⁻¹) is approximate. The true degeneracy direction in the Planck posterior is more complex.

4. m_ββ depends on Majorana phases which are unknown. The quoted range assumes maximal constructive interference; the minimum could be lower.