V2.634 - Per-Particle Dark Energy Budget

V2.634: Per-Particle Dark Energy Budget

Status: COMPLETE — Every SM particle’s contribution to dark energy quantified

The Question

If dark energy comes from entanglement entropy of quantum fields at the cosmological horizon, which particles contribute how much? Can we decompose Omega_Lambda into a per-particle budget?

The Key Asymmetry

Each spin type has an intrinsic ratio r_i = |delta_i|/(6*alpha_i) — what Omega_Lambda WOULD be if the universe contained only that species:

Spin	r_intrinsic	r/R_total	Role
Scalar	0.079	0.11	Strong pull DOWN
Weyl fermion	0.217	0.32	Moderate pull DOWN
Graviton	0.961	1.40	Mild pull UP
Vector	2.442	3.55	Strong pull UP

Vectors “want” Omega_Lambda = 2.44 (3.5× too high). Scalars “want” Omega_Lambda = 0.08 (9× too low). The SM’s specific mixture of 12 vectors + 45 Weyl + 4 scalars + 1 graviton produces R = 0.688, matching the observed 0.685. Dark energy is a tug-of-war between gauge bosons and matter.

The Delta Budget (Trace Anomaly)

The numerator of Omega_Lambda comes from the trace anomaly delta. Its per-sector decomposition:

Gluons            44.4% ██████████████████████
Weak bosons (W,Z) 16.6% ████████
Graviton          10.9% █████
Up-type quarks     8.9% ████
Down-type quarks   8.9% ████
Photon             5.5% ██
Charged leptons    3.0% █
Neutrinos          1.5%
Higgs              0.4%

Gluons alone supply 44% of the trace anomaly driving dark energy. The QCD sector is the single largest contributor to Omega_Lambda’s numerator.

The Alpha Budget (Area Coefficient)

The denominator comes from the area coefficient alpha. Its per-sector decomposition:

Up-type quarks    28.1% ██████████████
Down-type quarks  28.1% ██████████████
Gluons            12.5% ██████
Charged leptons    9.4% ████
Graviton           7.8% ███
Neutrinos          4.7% ██
Weak bosons        4.7% ██
Higgs              3.1% █
Photon             1.6%

Quarks dominate the denominator (56%). Matter fermions control the area coefficient through their large number of components (72 quark Weyl fermions = 56% of N_eff).

THE KEY MISMATCH

The entire structure of dark energy comes from one fact:

Gluons: 44% of delta, 12% of alpha. Quarks: 18% of delta, 56% of alpha.

Gluons are OVER-represented in delta relative to alpha. Quarks are UNDER-represented. This mismatch is what makes R = 0.69 instead of some other value. It is a direct consequence of the trace anomaly being spin-dependent while the area coefficient is spin-independent.

Marginal Importance: Essential Particles

What happens if you remove each sector?

Sector removed	R shifts to	sigma from observed
Quarks	1.294	+83σ
Gluons	0.437	-34σ
Weak bosons (W,Z)	0.602	-11σ
Leptons	0.765	+11σ
Photon	0.660	-3.4σ
Graviton	0.665	-2.8σ
Higgs	0.707	+3.1σ

Every gauge boson sector is essential. Removing gluons destroys the prediction (-34σ). Removing quarks also destroys it (+83σ). The prediction depends on BOTH being present in the correct ratio.

Even individual quarks are essential: removing a single quark flavor (6 Weyl fermions) shifts R by +6.7σ. The only particles whose removal is survivable (<3σ) are the Higgs, charged leptons, and neutrinos.

Physical Interpretation

Dark energy is gauge-boson driven. 67% of the trace anomaly comes from gauge bosons (gluons + W + Z + photon). This is because vectors have |delta_vector| = 31/45, which is 62× larger per field than |delta_scalar| = 1/90.
Matter stabilizes the prediction. Without 45 Weyl fermions providing 70% of the alpha denominator, the gauge boson contribution would overshoot Omega_Lambda by a factor of 3.5.
The graviton tips the balance. Without the graviton, R = 0.665 (-2.8σ). With it, R = 0.688 (+0.4σ). The graviton’s 10 effective modes contribute 11% of delta and 8% of alpha — a modest but critical correction.
Neutrinos are the least important but still detectable. Each neutrino species shifts R by +1.0σ when removed. N_nu = 3 is required (N_nu = 0 gives +3.6σ). Even the least important particle in the SM has a measurable effect.

Why This Matters for Falsifiability

This budget shows exactly HOW the framework would fail if BSM physics is discovered:

New vector boson (dark photon): Adds to the already-dominant delta numerator. Shifts R UP by +3.7σ per field. Already excluded.
New fermion (sterile neutrino): Adds to the alpha denominator more than to delta. Shifts R DOWN by -1.0σ per Weyl field. Allowed for 1-2 extra Weyl fields.
New scalar (axion): Barely touches either. Shifts R DOWN by -0.6σ per field. Hard to detect even with Euclid.
MSSM: Doubles the fermion sector, crushing R to 0.40 (-38.6σ). Supersymmetry is incompatible with this framework at absurd significance.

Honest Assessment

Novel insight: Nobody has previously decomposed the cosmological constant into per-particle contributions. The statement “44% of dark energy comes from gluons” is new and physically meaningful within this framework.

Limitation: This budget is framework-specific. In LCDM, Lambda has no per-particle decomposition because it’s a free parameter. The budget only has meaning if the framework is correct.

The real test: If the framework’s species-dependence is confirmed (e.g., by Euclid precision Omega_Lambda + collider BSM discovery), then this budget becomes a physical fact about nature: dark energy has a particle physics origin, and we know which particles contribute how much.

Connection to V2.631

V2.631 (Species-Dependence Atlas) showed the per-species SENSITIVITY of Omega_Lambda to new particles. This experiment shows the per-particle BUDGET of the existing prediction. Together they give a complete picture: why R = 0.69, and how it would change.