V2.652 - N_eff–Ω_Λ Falsification Corridor
V2.652: N_eff–Ω_Λ Falsification Corridor
The Idea
In ΛCDM, the cosmological N_eff (radiation content) and Ω_Λ (dark energy) are independent parameters. Any point in the (N_eff, Ω_Λ) plane is allowed.
In this framework, they are correlated: every new relativistic species shifts BOTH N_eff (through radiation density) AND Ω_Λ (through the trace anomaly formula R = |δ|/(6α)). This creates a narrow 1D corridor in the 2D parameter plane.
The corridor is spin-dependent — scalars, fermions, and vectors define rays in different directions from the SM point. The bundle of all rays is the framework’s allowed region.
Results
The Corridor Slopes
| Species type | ΔN_eff per field | ΔΩ_Λ per field | Slope dΩ_Λ/dN_eff | Direction |
|---|---|---|---|---|
| Real scalar (axion) | +0.571 | -0.00472 | -0.0083 | ↘ DOWN |
| Weyl fermion (sterile ν) | +1.000 | -0.00725 | -0.0072 | ↘ DOWN |
| Dirac fermion | +2.000 | -0.01428 | -0.0071 | ↘ DOWN |
| Vector boson (dark photon) | +1.143 | +0.02699 | +0.0236 | ↗ UP |
Key insight: Scalars and fermions decrease Ω_Λ while increasing N_eff. Vectors increase BOTH. The corridor fans out from the SM point, but only through a 1.8° arc.
Corridor Geometry
- Angular width: 1.8° out of 360°
- 99.5% of the (N_eff, Ω_Λ) plane is excluded
- Information content: 7.6 bits over ΛCDM
- In ΛCDM, the full 2D plane is allowed (0 bits of constraint)
Experimental Separation: SM vs SM + 1 species (Mahalanobis σ)
| Experiment | +1 scalar | +1 Weyl | +1 Dirac | +1 vector |
|---|---|---|---|---|
| Planck 2018 | 3.4σ | 5.9σ | 11.8σ | 8.5σ |
| Planck + BAO | 3.8σ | 6.7σ | 13.4σ | 10.7σ |
| CMB-S4 | 19.3σ | 33.8σ | 67.7σ | 39.8σ |
| CMB-S4 + Euclid | 19.1σ | 33.4σ | 66.7σ | 42.8σ |
Already with Planck: a single Weyl fermion is separated at 5.9σ in the joint plane. CMB-S4 makes this absurdly decisive (33σ+).
The breakdown for CMB-S4 + Euclid reveals that N_eff dominates for fermions (33σ from N_eff alone vs 3.6σ from Ω_Λ alone), but for vectors the joint test matters (38σ + 14σ → 43σ joint).
Neutrino Mass Prediction
The framework fixes Ω_Λ = 0.6877, which breaks the Ω_Λ–Σm_ν degeneracy:
| Experiment | Σm_ν (conditional) | From NH min (0.058 eV) | From IH min (0.102 eV) |
|---|---|---|---|
| Planck 2018 | 0.044 ± 0.052 eV | -0.3σ | -1.1σ |
| Euclid | 0.045 ± 0.018 eV | -0.7σ | -3.1σ |
Normal hierarchy preferred. With Euclid, inverted hierarchy excluded at 3.1σ, NH vs IH separation at 2.4σ.
Caveat: The conditional mean (0.045 eV) falls slightly below the oscillation minimum (0.058 eV). With current uncertainties this is only -0.7σ — not significant. But at higher precision, this becomes a self-consistency test of the framework itself. A more rigorous analysis using full Planck MCMC chains (non-Gaussian posterior near Σm_ν = 0) would refine this.
Falsification Scenarios
| If CMB-S4 measures… | Framework says… |
|---|---|
| N_eff = 3.044 (SM exact) | Ω_Λ = 0.6877. Framework confirmed. |
| N_eff = 3.5 | 0.46 sterile ν OR 0.80 axions. Ω_Λ must shift to 0.684. |
| N_eff = 4.0 | 0.96 sterile ν OR 0.48 Dirac. Ω_Λ must shift to 0.681. |
| If Euclid measures… | Framework says… |
|---|---|
| Ω_Λ = 0.690 ± 0.002 | 1.1σ tension. Compatible with ~0.08 dark vectors. |
| Ω_Λ = 0.680 ± 0.002 | 3.9σ tension. Needs ~1 sterile ν; check N_eff simultaneously. |
The JOINT test is the key: if Euclid finds Ω_Λ = 0.680 AND CMB-S4 finds N_eff = 3.044, the framework is falsified — no species can explain a downward Ω_Λ shift without increasing N_eff.
What Makes This Unique
-
No other framework predicts an N_eff–Ω_Λ correlation. ΛCDM, quintessence, modified gravity — all treat these as independent. The correlation IS the prediction.
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The corridor is absurdly narrow. 1.8° out of 360° means 99.5% of parameter space is excluded. A random framework would have zero correlation and cover the whole plane.
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The slope is spin-dependent. If a new species is discovered, the framework predicts not just that Ω_Λ shifts, but by HOW MUCH and in WHICH DIRECTION. A scalar shifts differently from a fermion, which shifts differently from a vector. The direction in the (N_eff, Ω_Λ) plane identifies the spin of the new particle.
-
Neutrino mass hierarchy prediction. By fixing Ω_Λ, the framework constrains Σm_ν and prefers normal hierarchy — a prediction that JUNO and DESI will test by 2028.
Honest Assessment
- The Mahalanobis separations are dominated by N_eff precision (CMB-S4’s ±0.03 is extraordinary). The Ω_Λ dimension adds modest additional discrimination.
- The neutrino mass prediction depends on approximate Fisher matrix modeling of the Planck posterior. The real constraint requires full MCMC analysis.
- The corridor assumes all new species are thermalized at T_ν. Partially decoupled species (smaller ΔN_eff) widen the corridor.
- The 99.5% exclusion fraction sounds dramatic but assumes only the cataloged species types exist. Exotic states (e.g., higher-spin fields) would add new rays.
Files
src/neff_corridor.py: Corridor geometry, species catalog, Fisher analysistests/test_neff_corridor.py: 20 tests, all passingresults.json: Full numerical output