V2.732: Neutrino Mass from Fixed Lambda — Breaking the OL-mnu Degeneracy

Status: COMPLETE — Two zero-parameter predictions, five falsification triggers

Motivation

The framework fixes Omega_Lambda = 0.6877 from the SM trace anomaly. In standard LCDM cosmological fitting, Omega_Lambda is degenerate with the neutrino mass sum Sigma_m_nu: heavier neutrinos suppress structure formation, shifting the inferred Omega_Lambda downward. By FIXING Omega_Lambda, the framework breaks this degeneracy.

This creates a chain of zero-parameter predictions:

SM field content → delta = -149/12 → Omega_Lambda = 0.6877 → H_0, m_nu bounds

No other cosmological framework makes this connection.

Method

1. Fix Omega_Lambda = 0.6877 (framework prediction)
2. Combine with Planck measurements of Omega_m h^2 = 0.1430 ± 0.0011 and Omega_b h^2 = 0.02237 ± 0.00015
3. Derive H_0, Omega_m, Omega_b, Omega_CDM, age of universe
4. Use the Planck Omega_Lambda–m_nu degeneracy to extract neutrino mass constraints
5. Compare with all current observations

Key Results

1. H_0 Prediction

Source	H_0 [km/s/Mpc]	Tension with framework
Framework	67.67 ± 0.26	—
Planck LCDM	67.36 ± 0.54	0.5σ
SH0ES	73.04 ± 1.04	5.0σ

The framework predicts H_0 = 67.67 km/s/Mpc with uncertainty ±0.26 km/s/Mpc (half the Planck uncertainty, because Omega_Lambda is exact rather than fitted).

The Hubble tension is NOT resolved. The framework predicts that the tension must be due to systematic errors in local distance measurements, not new physics. If H_0 > 70 is confirmed, the framework is falsified: accommodating H_0 = 73 would require Omega_m h^2 = 0.166, which is 21σ from the Planck measurement.

2. Neutrino Mass Constraint

The framework’s higher Omega_Lambda (0.6877 vs 0.6847) shifts the preferred neutrino mass downward along the degeneracy direction:

Analysis	Framework preferred Σm_ν	Uncertainty
CMB-only	0.045 eV	±0.037 eV
CMB+BAO	0.022 eV	±0.050 eV

Normal hierarchy minimum (0.06 eV) is perfectly consistent.

3. Neutrino Mass Windows

Σm_ν scenario	Tension with framework
Normal hierarchy min (0.06 eV)	0.4σ — preferred
Inverted hierarchy min (0.10 eV)	1.5σ — allowed
Quasi-degenerate (0.15 eV)	2.9σ — disfavored
KATRIN limit (0.20 eV)	4.3σ — excluded
Planck 95% CL (0.12 eV)	2.1σ — marginal

The framework prefers light neutrinos (Σm_ν < 0.12 eV at 2σ). Combined with V2.326 (Majorana preferred over Dirac at 2.1σ), the framework predicts: 3 light Majorana neutrinos in normal hierarchy.

4. Complete Zero-Parameter Prediction Table

All derived from ONE input: Omega_Lambda = 0.6877

Observable	Prediction	Current observation	Tension
Omega_Lambda	0.6877	0.6847 ± 0.0073	0.4σ
H_0 [km/s/Mpc]	67.67	67.36 ± 0.54	0.5σ
w_0	-1 (exact)	-1.03 ± 0.04	0.8σ
w_a	0 (exact)	-0.1 ± 0.3	0.3σ
Σm_ν [eV]	0.045	< 0.12 (95%)	OK
Omega_m	0.3123	0.3153 ± 0.007	-0.4σ
t_0 [Gyr]	13.77	13.80 ± 0.02	-1.3σ
H_0 vs SH0ES	67.67	73.04 ± 1.04	5.0σ

Every prediction consistent with current data, except the Hubble tension (which the framework predicts must be systematic).

5. The Omega_Lambda–m_nu Degeneracy

Scanning Σm_ν from 0 to 0.30 eV along the Planck degeneracy direction:

• Σm_ν = 0.04 eV: framework at -0.1σ (sweet spot)
• Σm_ν = 0.06 eV: framework at +0.4σ
• Σm_ν = 0.12 eV: framework at +2.1σ (boundary)
• Σm_ν = 0.20 eV: framework at +4.3σ (excluded)
• Σm_ν = 0.30 eV: framework at +7.0σ (strongly excluded)

The heavier the neutrinos, the more the framework is disfavored.

6. Falsification Triggers

The experiment identifies five independent falsification conditions:

1. Omega_Lambda ≠ 0.6877 ± 0.01 → framework falsified
2. H_0 ≠ 67.7 ± 0.3 → framework falsified (if Omega_m h^2 stable)
3. Σm_ν > 0.15 eV → >2.9σ tension with framework
4. Neutrinos are Dirac → 2.1σ disfavored (V2.326)
5. Inverted hierarchy confirmed → 1.5σ disfavored

7. Future Tests

Experiment	Observable	Discrimination power
Euclid (2032)	σ(Ω_Λ) = 0.002	1.5σ on Ω_Λ
CMB-S4 (2030)	σ(Ω_Λ) = 0.003	1.0σ on Ω_Λ
DESI 5yr (2028)	σ(Ω_Λ) = 0.003	1.0σ on Ω_Λ
KATRIN final	σ(m_ν) = 0.20 eV	Direct mass
Project 8	σ(m_ν) = 0.04 eV	Direct mass
JUNO (2026)	Mass ordering	Hierarchy test

The most powerful near-term test: JUNO (2026) will determine the mass ordering. If inverted hierarchy is confirmed, the framework takes a 1.5σ hit.

The Unique Prediction

No other cosmological theory predicts all of the following from a SINGLE calculation:

1. Ω_Λ = 0.6877 (from trace anomaly delta = -149/12)
2. H_0 = 67.67 km/s/Mpc (from Ω_Λ + CMB)
3. Σm_ν < 0.12 eV (from Ω_Λ-m_ν degeneracy breaking)
4. Normal hierarchy preferred
5. Majorana neutrinos preferred
6. Hubble tension must be systematic

This is a JOINT prediction: failure of any link falsifies the entire chain.

Honest Assessment

Strengths:

• Zero-parameter predictions consistent with ALL current observations
• H_0 prediction has half the uncertainty of Planck’s LCDM fit
• Neutrino mass constraint from particle physics → cosmology chain is unique
• Multiple independent falsification triggers with near-term experiments

Weaknesses:

• The degeneracy-breaking relies on the approximate Planck OL-mnu slope
• A full MCMC analysis (with CosmoMC/MontePython) would give more precise results
• The framework does NOT resolve the Hubble tension — it predicts it’s systematic
• If SH0ES H_0 is confirmed as physical, the framework is in serious trouble

What this means for the program: The framework now has a complete prediction chain from particle physics to cosmological observables, including neutrino properties. The chain is falsifiable at every link, with experiments running or planned within the next decade.