V2.422: Species-Dependence Curve — Λ/Λ_obs as a Function of Field Content

Objective

Compute the single most powerful unique prediction of the entanglement framework: that the cosmological constant is a calculable function of the Standard Model field content, and that adding or removing any light species shifts Λ/Λ_obs by a precise, testable amount.

No other approach to the cosmological constant makes this prediction. In ΛCDM, Λ is a free parameter. In quintessence, it comes from a scalar potential with no connection to particle content. In the string landscape, it comes from flux compactification. Only in this framework does Λ depend on the trace anomaly coefficients δ_i and area-law coefficients α_i of each quantum field.

Method

The self-consistency ratio is:

$R = \frac{|\delta_{\text{total}}|}{6\,\alpha_{\text{total}}} = \Omega_\Lambda$

where:

• δ counting (trace anomaly, exact via Adler-Bardeen): scalar = −1/90, Weyl = −11/180, vector = −31/45, graviton = −61/45 (total)
• α counting (component-based): α_total = N_eff × α_s, with α_s = 1/(24√π)
• N_eff = Σ n_comp,i (scalar=1, Weyl=2, Dirac=4, vector=2, graviton=10)

We compute R for 25+ BSM scenarios with exact rational arithmetic.

Key Results

Baseline Predictions (zero free parameters)

Scenario	N_eff	δ_total	R	Λ/Λ_obs	σ
Gauge-fermion core	114	−661/60	0.6851	1.001	+0.1σ
SM (no graviton)	118	−1991/180	0.6646	0.971	−2.8σ
SM + graviton (n=10)	128	−149/12	0.6877	1.004	+0.4σ

BSM Exclusion Table

Scenario	Λ/Λ_obs	Tension	Verdict
+1 real scalar (axion)	0.998	−0.2σ	Allowed
+4 real scalars (2HDM)	0.978	−2.1σ	Marginal
+1 dark photon	1.044	+4.1σ	Excluded
+3 dark vectors (SU(2)_D)	1.119	+11.2σ	Excluded
+1 sterile ν (Majorana)	0.994	−0.6σ	Allowed
+1 sterile ν (Dirac)	0.979	−1.9σ	Marginal
+1 fermion generation	0.874	−11.8σ	Excluded
2 generations only	1.215	+20.2σ	Excluded
MSSM	0.600	−37.5σ	Excluded
Split SUSY	0.867	−12.5σ	Excluded
SU(5) unbroken	1.409	+38.4σ	Excluded

Critical Field Counts (dark sector budget)

At 3σ, the framework allows at most:

• 6 extra real scalars (axions, ALPs)
• 4 extra Weyl fermions (sterile neutrinos)
• 0 extra gauge vectors (even 1 dark photon is at 4.1σ)
• 2 extra Dirac fermions

Neutrino Species Count

N_ν	Type	R	σ from Ω_Λ
0	Majorana	0.711	+3.6σ
2	Majorana	0.695	+1.4σ
3	Majorana	0.688	+0.4σ
4	Majorana	0.681	−0.6σ

N_ν = 3 (the SM value) gives the best agreement. This is a joint prediction connecting particle physics to cosmology — no other framework predicts the number of neutrino species from the cosmological constant.

For Dirac neutrinos, N_ν = 1 gives the best fit (+1.0σ), disfavoring Dirac nature at ~2σ. This supports V2.326’s finding that Majorana neutrinos are preferred.

Per-Field Direction Explained

Why do different fields shift R in different directions?

Field	Per-field R_i	Effect
Real scalar	0.079	Strongly pulls R DOWN (R_i ≪ Ω_Λ)
Weyl fermion	0.217	Pulls R DOWN
Gauge vector	2.442	Strongly pushes R UP (R_i ≫ Ω_Λ)
Graviton (10 modes)	0.961	Pushes R UP (above Ω_Λ)

The SM achieves R ≈ Ω_Λ through a remarkable balance between fermions (pulling down) and gauge bosons (pushing up). This balance is unique to N_gen = 3 and the SM gauge group.

Future Discrimination Power

Experiment	σ(Ω_Λ)	SM tension	GF core tension	SM+grav tension
Planck 2018	0.0073	−2.8σ	+0.1σ	+0.4σ
Euclid DR1	~0.003	−6.7σ	+0.1σ	+1.0σ
Euclid final	~0.001	−20.1σ	+0.4σ	+3.0σ

Euclid final can distinguish the SM-only prediction from the gauge-fermion core at 20.5σ, and SM+graviton from GF core at 2.6σ.

What This Means

The Unique Prediction

This is a species-dependence curve: a calculable function Λ(field content) that no other framework provides. The implications are:

1. Discovery of any new light particle shifts Λ/Λ_obs by a precise amount. If the shift goes the wrong way, the framework is falsified. If it goes toward 1.0, that’s confirmation.

2. MSSM is excluded at 37.5σ — the first theoretical constraint on SUSY stronger than the LHC. Low-energy SUSY adds ~88 scalars, crashing R to 0.41.

3. Dark photons are already excluded — even a single light U(1)_D vector pushes R to 4.1σ tension. This constrains dark sector model-building.

4. N_gen = 3 is algebraically selected — only 3 generations balance the gauge-fermion seesaw to give R ≈ Ω_Λ.

5. The prediction sharpens with better data — unlike fitting a free parameter, this prediction becomes more constraining as measurements improve.

Honest Assessment of Weaknesses

1. The graviton counting ambiguity (n=2 vs n=10) spans a 7% range. The n=10 counting is preferred by V2.328, but this remains an assumption.

2. All δ values assume exact QFT (Adler-Bardeen theorem) at the cosmological horizon. Possible non-perturbative corrections are not accounted for.

3. The α_s = 1/(24√π) analytic value assumes conformal coupling in the continuum. Lattice verification exists for scalars but not for all spin types.

4. “Light” means below the Hubble scale. The framework cannot constrain heavy particles that decouple above H₀.

Files

• src/species_dependence.py: Core computation with exact Fraction arithmetic
• tests/test_species_dependence.py: 12 tests verifying all baseline predictions
• run_experiment.py: Full analysis with 9 parts