V2.649 - Species-Dependence Curve — The Framework's Most Powerful Unique Prediction
V2.649: Species-Dependence Curve — The Framework’s Most Powerful Unique Prediction
Hypothesis
Every new light particle shifts Λ/Λ_obs by a calculable, species-dependent amount. No other framework makes this prediction. In ΛCDM, Λ is a free parameter. In quintessence, Λ depends on a potential. Here, Λ is determined by the Standard Model field content — period.
The formula: R = |δ_total| / (6 · α_s · N_eff), where both sums run over all light fields.
Results
The Species-Dependence Table
| Scenario | R | σ from obs | Λ/Λ_obs | Status |
|---|---|---|---|---|
| SM (no graviton) | 0.6646 | -2.76 | 0.971 | Lower bracket |
| SM + graviton | 0.6877 | +0.42 | 1.004 | Baseline |
| +1 real scalar (axion) | 0.6830 | -0.23 | 0.998 | Compatible |
| +1 complex scalar | 0.6784 | -0.87 | 0.991 | Compatible |
| +1 Weyl sterile ν | 0.6805 | -0.58 | 0.994 | Compatible |
| +1 Dirac sterile ν | 0.6735 | -1.54 | 0.984 | Marginal |
| +1 dark photon | 0.7147 | +4.11 | 1.044 | Excluded (4.1σ) |
| dark QED (γ’ + ψ’) | 0.6999 | +2.08 | 1.022 | Marginal |
| dark SU(2) | 0.7663 | +11.2 | 1.119 | Excluded |
| dark SU(3) | 0.8827 | +27.1 | 1.289 | Excluded |
| MDM: SU(2) 5-plet fermion | 0.6536 | -4.26 | 0.955 | Excluded (4.3σ) |
| MSSM (all sparticles light) | 0.4030 | -38.6 | 0.589 | Excluded (38.6σ) |
| axion + axino (SUSY) | 0.6714 | -1.82 | 0.981 | Marginal |
Neutrino Number Selection
| N_ν | R | σ from obs | Status |
|---|---|---|---|
| 0 | 0.7109 | +3.59 | Excluded |
| 1 | 0.7029 | +2.50 | Excluded |
| 2 | 0.6952 | +1.44 | Marginal |
| 3 | 0.6877 | +0.42 | Selected |
| 4 | 0.6805 | -0.58 | Allowed (but not preferred) |
| 5 | 0.6735 | -1.54 | Marginal |
| 6 | 0.6667 | -2.47 | Excluded |
N_ν = 3 is uniquely selected as the best fit. N_ν = 4 is currently allowed at 0.58σ, but Euclid will separate them at 3.6σ.
Species Sensitivity (dR per field)
| Field type | dR per field | Equivalent σ-shift |
|---|---|---|
| Scalar | -0.00472 | -0.65σ |
| Weyl fermion | -0.00725 | -0.99σ |
| Vector boson | +0.02699 | +3.70σ |
| Graviton | +0.01981 | +2.71σ |
Key insight: Scalars and fermions decrease R (push toward lower Λ), while vectors and gravitons increase R (push toward higher Λ). The SM sits at a near-exact balance point. This is not engineered — it follows from the trace anomaly coefficients being what they are.
Exclusion Limits (current Planck precision)
| Field type | Max additional fields (2σ) |
|---|---|
| Scalars | 3 |
| Weyl fermions | 2 |
| Vector bosons | 0 |
A single extra light vector boson is excluded at 4.1σ. This is the sharpest constraint.
Experimental Forecasts
| Experiment | σ(Ω_Λ) | SM+grav tension | Max extra scalars | N_ν=3 vs 4 separation |
|---|---|---|---|---|
| Planck 2018 | 0.0073 | 0.4σ | 3 | 1.0σ |
| DESI Y5 (2028) | 0.003 | 1.0σ | 1 | 2.4σ |
| Euclid (2030) | 0.002 | 1.5σ | 1 | 3.6σ |
| CMB-S4 + Euclid | 0.001 | 3.0σ | 0 | 7.2σ |
Black Hole Entropy Log Correction
| Approach | δ_BH | Species-dependent? |
|---|---|---|
| This framework | -149/12 ≈ -12.42 | Yes |
| Loop quantum gravity | -3/2 = -1.50 | No (universal) |
| String theory | varies | Depends on compactification |
The predictions differ by a factor of 8.3. This is a clean discriminant against LQG, which predicts a universal log correction independent of the matter content.
Electroweak Phase Transition Invariance
- Unbroken phase: δ = -149/12, N_eff = 128, R = 0.6877
- Broken phase: δ = -149/12, N_eff = 128, R = 0.6877
- ΔR = 0 exactly (Stueckelberg decomposition conserves field count)
Standard QFT predicts a vacuum energy jump of ~(246 GeV)⁴ at the EW transition. This framework predicts zero change in Λ. LISA observations of the EW transition gravitational wave background could in principle distinguish these.
The Honest Tension
At ultimate precision (CMB-S4 + Euclid, σ = 0.001), the SM+graviton prediction R = 0.6877 would be 3.0σ from the current central value Ω_Λ = 0.6847. The exact N_eff that gives Ω_Λ_obs is 128.57, while SM+graviton gives 128. This 0.44% mismatch is below current sensitivity but will eventually become testable.
Possible resolutions:
- The Planck central value shifts upward (currently R = 0.6877 is at +0.4σ, well within errors)
- Graviton edge modes contribute slightly less than n_grav = 10 (see V2.328: n_grav = 10.6 ± 1.4)
- Higher-order corrections to α_s or the graviton trace anomaly
- The framework is wrong (maximally falsifiable prediction)
This is a feature, not a bug. A framework that cannot be falsified is not physics.
What This Means
Unique predictions no other framework makes:
- Λ/Λ_obs = 1.004 from zero free parameters — the only approach that calculates the cosmological constant from known particle physics
- Every BSM particle shifts Λ by a calculable amount — immediate confrontation with any new particle discovery
- N_ν = 3 preferred from cosmological constant alone — a joint prediction connecting particle physics to cosmology
- MSSM excluded at 38.6σ if all sparticles are light — the strongest theoretical exclusion of low-scale SUSY
- Zero extra light vectors allowed — any dark photon discovery below the Hubble scale falsifies the framework
- BH log correction = -149/12 vs LQG’s -3/2 — an 8× discriminant against loop quantum gravity
- Λ unchanged through EW transition — no 10⁵⁶ fine-tuning, testable via LISA
The sharpest near-term test:
Euclid (2030) will separate N_ν = 3 from N_ν = 4 at 3.6σ. If a fourth neutrino species is discovered below the Hubble scale, the framework’s prediction shifts from +0.42σ to -0.58σ — still allowed. But a fifth species pushes to -1.54σ, and a sixth to -2.47σ. The framework provides a particle-by-particle accountability ledger.
Files
src/species_curve.py: All calculations (exact arithmetic viafractions.Fraction)tests/test_species_curve.py: 28 tests, all passingresults.json: Full numerical output