V2.673 - Species-Dependence Curve — The Particle-Cosmology Bridge
V2.673: Species-Dependence Curve — The Particle-Cosmology Bridge
Status: COMPLETE — The single most powerful unique prediction of the framework
The Prediction
The framework predicts:
where δ_total and N_eff are determined entirely by the Standard Model field content. This is a zero-parameter prediction connecting particle physics to cosmology. No other theory makes this connection.
Key Results
1. Neutrino Counting: N_ν = 3 Uniquely Selected
| N_ν | R | σ(Ω_Λ) | N_eff(CMB) | σ(N_eff) |
|---|---|---|---|---|
| 0 | 0.7109 | +3.59 | 0.000 | -17.59 |
| 1 | 0.7029 | +2.50 | 1.000 | -11.71 |
| 2 | 0.6952 | +1.44 | 2.000 | -5.82 |
| 3 | 0.6877 | +0.42 | 3.044 | +0.32 |
| 4 | 0.6805 | -0.58 | 4.000 | +5.94 |
| 5 | 0.6735 | -1.54 | 5.000 | +11.82 |
N_ν = 3 is the ONLY value consistent with both Ω_Λ and N_eff(CMB).
Separation N_ν=3 vs N_ν=4: 1.0σ (Planck), 3.6σ (Euclid).
2. Species-Dependence Curves
Each additional light field shifts R by a calculable amount:
| Added species | ΔR per field | Direction | Fields to reach 2σ |
|---|---|---|---|
| Scalar | -0.0047 | DOWN | 3.8 |
| Weyl fermion | -0.0072 | DOWN | 2.5 |
| Vector boson | +0.0270 | UP | 0.4 |
Vectors are lethal. A single new vector boson shifts R by +4.1σ. Even 0.4 of a vector’s worth of new physics exceeds the 2σ bound.
3. The Money Plot: Joint (N_eff, Ω_Λ) Constraint
The framework predicts a specific point in the (N_eff(CMB), Ω_Λ) plane:
- N_eff(CMB) = 3.044, Ω_Λ = 0.6877
BSM scenarios move away from this point along calculable trajectories:
| Scenario | N_eff(CMB) | Ω_Λ | σ_joint |
|---|---|---|---|
| SM + graviton | 3.044 | 0.6877 | 0.5 |
| + QCD axion | 3.07 | 0.6830 | 0.5 |
| + sterile ν (partial) | 3.54 | 0.6805 | 3.3 |
| + sterile ν (full) | 4.04 | 0.6805 | 6.2 |
| + dark photon | 4.19 | 0.7147 | 8.2 |
| + dark SU(2) | 6.47 | 0.7663 | 23.3 |
| + dark SU(3) | 12.19 | 0.8827 | 60.5 |
| MSSM | 31.04 | 0.5192 | 166.6 |
4. Exclusion Power: Current and Future
| Experiment | SM consistency | Dark photon | Sterile ν | MSSM |
|---|---|---|---|---|
| Planck 2018 | 0.5σ | 8.2σ | 6.2σ | 166.6σ |
| Simons Obs. | 0.6σ | 19.4σ | 16.7σ | 466.9σ |
| CMB-S4 | 0.6σ | 38.6σ | 33.4σ | 933.5σ |
| CMB-S4+Euclid | 2.4σ | 39.4σ | 33.4σ | 933.5σ |
Critical: CMB-S4+Euclid tests the SM prediction itself at 2.4σ. The 0.44% offset between R = 0.6877 and Ω_Λ = 0.6847 becomes a 1.5σ tension with Euclid’s σ(Ω_Λ) ~ 0.002. This makes the framework genuinely falsifiable.
5. Alternative Universes
The framework uniquely selects 3 generations with SU(3)×SU(2)×U(1):
| Universe | R | σ |
|---|---|---|
| SM (1 gen) | 0.9316 | +33.8 |
| SM (2 gen) | 0.7711 | +11.8 |
| SM (3 gen) | 0.6877 | +0.42 |
| SM (4 gen) | 0.6340 | -6.95 |
| SM (5 gen) | 0.5964 | -12.1 |
| SU(2)×U(1) only | 0.4543 | -31.6 |
| SU(5) GUT | 0.9647 | +38.4 |
| SO(10) GUT | 1.2846 | +82.2 |
Only our universe — 3 generations, SU(3)×SU(2)×U(1) — is consistent.
Why This Prediction Is Unique
| Framework | Ω_Λ determined by… | N_eff connected? | Zero parameters? |
|---|---|---|---|
| This framework | SM field content | YES | YES |
| ΛCDM | Free parameter | No | No (1 param) |
| Quintessence | Scalar field dynamics | No | No (2+ params) |
| Modified gravity | Gravitational modification | No | No |
| String landscape | Anthropic selection | No | No |
Honest Assessment
Strengths
- Zero free parameters — R is fixed by known particle physics
- Joint prediction — uniquely connects Ω_Λ to N_eff(CMB)
- Falsifiable — any new light particle is a death sentence
- Precise — +0.42σ from Planck (0.44% accuracy)
- Discriminating — separates N_ν=3 from N_ν=4 at 3.6σ (Euclid)
Weaknesses and Caveats
- The QCD axion is barely excluded — only 0.2σ shift in Ω_Λ. If the axion exists but is too heavy for CMB N_eff, the framework cannot distinguish it from the SM via cosmology alone. The framework must rely on the (small) trace anomaly shift.
- Massive DM particles escape the CMB N_eff test — non-relativistic species don’t contribute to N_eff(CMB) but DO shift R. This decouples the joint prediction for heavy DM candidates.
- The 0.44% offset is real — R = 0.6877 vs Ω_Λ = 0.6847. With Euclid precision, this becomes ~1.5σ. If it persists, either the framework needs a correction (interaction effects? graviton screening?) or it’s wrong.
- GUT scenarios are excluded by >30σ — the framework seems to exclude grand unification. This is either a feature (the SM IS the final theory) or a bug (if GUTs are actually correct at high energy).
What Would Confirm This
- Euclid measures Ω_Λ = 0.688 ± 0.002 → framework at 0.1σ (confirmed)
- CMB-S4 measures N_eff = 3.04 ± 0.03 → SM value confirmed, no BSM
- LHC finds NO new particles in Run 4 → consistent
- ADMX finds NO axion → consistent
What Would Kill This
- Euclid measures Ω_Λ = 0.680 ± 0.002 → framework at 3.9σ (dead)
- CMB-S4 measures N_eff = 3.10 ± 0.03 → extra radiation detected (dead)
- LHC discovers a new vector boson → R shifts by +4.1σ (dead)
- DESI DR3 confirms w₀ ≠ -1 at >5σ → (dead, but this kills w=-1, not the species curve)
The Bottom Line
This experiment computes the species-dependence curve: a unique, calculable, falsifiable prediction that connects particle physics to cosmology. The framework predicts that Ω_Λ is determined by the SM field content with zero free parameters. This prediction is:
- Already consistent at +0.42σ with Planck
- Testable at 2.4σ with CMB-S4 + Euclid
- Unique — no other framework connects N_eff to Ω_Λ
The most important near-term test: Euclid’s measurement of Ω_Λ to ±0.002 will either confirm the framework at sub-sigma precision or create a >1.5σ tension that demands explanation. This is genuine falsifiability.