V2.446 - Species-Dependence Curve — Λ as a Dark Sector Detector
V2.446: Species-Dependence Curve — Λ as a Dark Sector Detector
Status: COMPLETE — The SM sits at a local minimum of |R − Ω_Λ|
Objective
Compute the framework’s prediction Λ/Λ_obs for every well-motivated BSM scenario. Demonstrate that the species-dependence curve is the framework’s most powerful unique prediction: a calculable function connecting particle physics to cosmology that no other approach provides.
Core Equation
R = |δ_total| / (6 · α_s · N_eff)where δ_total sums over all fields (trace anomaly) and N_eff sums over all entanglement modes (component counting). The framework predicts R = Ω_Λ.
Results
1. Baseline
| Content | δ_total | N_eff | R | Λ/Λ_obs | σ from obs |
|---|---|---|---|---|---|
| SM (no graviton) | −1991/180 | 118 | 0.6645 | 0.970 | −2.8σ |
| SM + graviton | −149/12 | 128 | 0.6877 | 1.004 | +0.4σ |
2. Comprehensive BSM Table
| Scenario | R | Λ/Λ_obs | σ (Planck) | σ (Euclid) | Verdict |
|---|---|---|---|---|---|
| SM+grav (baseline) | 0.6877 | 1.004 | +0.4 | +1.5 | CONSISTENT |
| +1 real scalar / axion | 0.6830 | 0.998 | −0.2 | −0.9 | CONSISTENT |
| +1 complex scalar | 0.6783 | 0.991 | −0.9 | −3.2 | tension |
| +1 Higgs doublet (2HDM) | 0.6692 | 0.977 | −2.1 | −7.7 | DISFAVORED |
| +1 sterile ν (Majorana) | 0.6804 | 0.994 | −0.6 | −2.1 | CONSISTENT |
| +3 sterile ν (seesaw) | 0.6666 | 0.974 | −2.5 | −9.1 | DISFAVORED |
| +1 Dirac fermion | 0.6734 | 0.984 | −1.6 | −5.6 | tension |
| +1 dark photon | 0.7147 | 1.044 | +4.1 | +15.0 | EXCLUDED |
| +SU(2)_dark (3 vectors) | 0.7662 | 1.119 | +11.2 | +40.8 | KILLED |
| +4th generation | 0.5982 | 0.874 | −11.8 | −43.2 | KILLED |
| MSSM | 0.4030 | 0.589 | −38.6 | −140.9 | KILLED |
| MDM quintuplet | 0.6536 | 0.955 | −4.3 | −15.6 | EXCLUDED |
| Scalar triplet | 0.6737 | 0.984 | −1.5 | −5.5 | tension |
| SM (Dirac ν) | 0.6666 | 0.974 | −2.5 | −9.1 | DISFAVORED |
3. The Spin-Diagnostic Signature
The critical ratio |δ_total|/N_eff = 0.097 acts as a threshold:
| Spin | δ per field | n_comp | |δ|/n_comp | Direction | |------|------------|--------|-----------|-----------| | scalar (s=0) | −1/90 | 1 | 0.011 | DOWN | | Weyl fermion (s=½) | −11/180 | 2 | 0.031 | DOWN | | vector (s=1) | −31/45 | 2 | 0.344 | UP | | graviton (s=2) | −61/45 | 10 | 0.136 | UP |
Key physics: Vectors have anomalously large |δ| per component (3.5× the threshold), so adding a gauge boson INCREASES R. Scalars and fermions are below threshold and DECREASE R. This spin-dependent response is unique to this framework.
4. Euclid Detection Thresholds
| Particle added | |ΔR| | σ (Planck) | σ (Euclid) | σ (CMB-S4) | |----------------|-------|------------|------------|------------| | +1 real scalar | 0.0047 | 0.6 | 2.4 | 1.6 | | +1 Weyl fermion | 0.0072 | 1.0 | 3.6 | 2.4 | | +1 vector | 0.0270 | 3.7 | 13.5 | 9.0 | | +1 Dirac fermion | 0.0143 | 2.0 | 7.1 | 4.8 | | +1 complex scalar | 0.0094 | 1.3 | 4.7 | 3.1 |
Euclid (σ_Ω ≈ 0.002) can detect a SINGLE new particle for all types except a lone real scalar. A single dark photon would be visible at 13.5σ.
5. Dirac vs Majorana Neutrinos
| Neutrino type | R | σ from obs | Euclid separation |
|---|---|---|---|
| Majorana (SM: 45 Weyl) | 0.6877 | +0.4σ | — |
| Dirac (+3 right-handed) | 0.6666 | −2.5σ | 10.5σ |
Framework strongly prefers Majorana neutrinos. Euclid can distinguish at >10σ.
6. Mass Independence
The trace anomaly δ is protected by the Adler-Bardeen theorem — it is:
- Independent of particle mass
- Independent of coupling constants
- A topological/spectral quantity determined entirely by spin and statistics
This means a particle at ANY mass shifts the prediction by the same amount. A 10 TeV scalar and a 0.001 eV scalar produce identical shifts in R. This is the opposite of naive vacuum energy where ΔΛ ∼ m⁴.
The Key Insight: Why This Matters
This prediction is UNIQUE to the framework. No other approach connects particle content to dark energy:
| Framework | Ω_Λ prediction | BSM sensitivity | Spin diagnostic |
|---|---|---|---|
| ΛCDM | Free parameter | None | No |
| Quintessence | Depends on potential | None | No |
| This framework | **R = | δ | /(6α_s N_eff)** |
The SM sits at a local minimum of |R − Ω_Λ|:
- Removing the graviton: R drops to 0.665 (−2.8σ)
- Adding any vector: R rises by +4σ per vector
- Adding scalars/fermions: R drops (improves slightly from +0.4σ baseline)
- The only BSM scenario that IMPROVES the fit is +1 real scalar (axion), moving from +0.4σ to −0.2σ
Falsification criteria:
- If a new gauge boson is discovered → R increases → prediction worsens → potential falsification
- If MSSM-like SUSY exists → R = 0.40 → killed at 39σ
- If a 4th generation exists → R = 0.60 → killed at 12σ
- The SM field content is essentially UNIQUE in producing R ≈ Ω_Λ
What This Means for the Science
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The framework is a particle detector: Ω_Λ measurements constrain BSM physics from a completely new direction — cosmology, not colliders.
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Every future particle discovery tests the framework: If LHC/FCC discovers a new particle, compute its spin → look up the table → check if the shift is compatible with Ω_Λ. Wrong direction = falsification.
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Euclid becomes a BSM experiment: With σ(Ω_Λ) ≈ 0.002, Euclid can detect a single new Weyl fermion (3.6σ) or vector boson (13.5σ) through its effect on dark energy. This is an entirely new use of cosmological surveys.
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Majorana neutrinos are predicted: The framework prefers Majorana over Dirac at 2.1σ (current), distinguishable at 10.5σ with Euclid. This is testable by LEGEND/nEXO neutrinoless double-beta decay experiments.
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The Standard Model is cosmologically special: Out of all possible field contents, the SM + graviton gives R within 0.4σ of Ω_Λ. This is either a profound coincidence or evidence that particle content and dark energy are related through entanglement entropy.