V2.425: Graviton Precision Prediction — Narrowing the Λ/Λ_obs Window

Objective

Pin down the graviton’s contribution to Λ and compute what experiments must measure to confirm or falsify the framework. The graviton mode counting (n=2 vs n=10) is the single largest uncertainty, spanning a 7% range in Λ/Λ_obs.

Key Results

The Prediction Curve R(n_grav)

R is a monotonically decreasing function of the number of graviton modes contributing to α:

n_grav	Counting scheme	R	Λ/Λ_obs	σ
0	No graviton (but δ_grav included)	0.7460	1.090	+8.4σ
2	TT-only	0.7336	1.071	+6.7σ
5	Massive graviton	0.7157	1.045	+4.2σ
10	Full covariant	0.6877	1.004	+0.4σ

TT-only (n=2) is excluded at 6.7σ. Full covariant counting (n=10) is preferred at +0.4σ.

Best-Fit n_grav from Ω_Λ

Inverting R(n_grav) = Ω_Λ_obs:

• n_grav = 10.6 ± 1.4 (Planck 2018)
• n=10 at −0.4σ from best fit
• n=2 at −6.3σ from best fit (excluded)

This confirms V2.328’s graviton spectroscopy result.

The Graviton Screening Fraction

The graviton contributes:

• 10.9% of δ (trace anomaly): f_δ = 244/2235
• 7.8% of N_eff (area law): f_α = 10/128

This asymmetry (δ > α fractionally) means the graviton raises R relative to the SM-only prediction. The δ contribution is topological (Adler-Bardeen protected); only the α contribution (mode counting) is uncertain.

The Higgs-Graviton Cancellation

With n=10, the Higgs and graviton nearly cancel:

	δ contribution	α contribution
Higgs (4 scalars)	−0.044	4 α_s
Graviton	−1.356	10 α_s
Net shift from GF core	ΔR = +0.0026	(0.38%)

This 98% cancellation is coincidental — no symmetry protects it. It means the gauge-fermion core (R = 0.6851) and SM+grav (R = 0.6877) give nearly identical predictions.

Full Cosmological Parameters

Parameter	Planck	GF core	SM+grav(10)	SM only
Ω_Λ	0.6847 ± 0.0073	0.6851 (+0.1σ)	0.6877 (+0.4σ)	0.6646 (−2.8σ)
H₀	67.36 ± 0.54	67.39 (+0.1σ)	67.67 (+0.6σ)	65.29 (−3.8σ)
σ₈	0.8111 ± 0.006	0.8108 (−0.0σ)	0.8091 (−0.3σ)	0.8237 (+2.1σ)
Age (Gyr)	13.797 ± 0.023	13.800 (+0.1σ)	13.775 (−1.0σ)	13.990 (+8.4σ)

SM-only gives wrong H₀ (−3.8σ) and wrong age (+8.4σ). Both GF core and SM+grav(10) pass all tests.

Euclid Discrimination Forecast

Experiment era	σ(Ω_Λ)	SM vs GF	GF vs SM+grav(10)	SM vs SM+grav(10)
Planck 2018	0.0073	2.8σ	0.4σ	3.2σ
Euclid DR1	0.003	6.9σ	0.9σ	7.7σ
Euclid final	0.001	20.6σ	2.6σ	23.2σ
Next-gen	0.0005	41.1σ	5.2σ	46.3σ

The precision target: σ(Ω_Λ) < 0.0013 distinguishes GF core from SM+grav at 2σ. Euclid final gets there; next-gen CMB-S4 + LSS at 5σ.

Falsification Window

The framework predicts Ω_Λ ∈ [0.6821, 0.6907] (the 3σ band spanning GF core to SM+grav at σ=0.001). If Euclid measures outside this 0.86% window, the framework is falsified.

What This Means

1. The graviton mode count is a measurable prediction: Ω_Λ selects n_grav = 10.6 ± 1.4. This is a statement about quantum gravity — the cosmological constant measures how many graviton modes entangle across the horizon.

2. n=2 (TT-only) is already excluded at 6.7σ: Only full covariant counting works. This rules out approaches that treat the graviton as having only 2 physical DOF for entanglement.

3. A tight falsification window: [0.682, 0.691] at Euclid precision. This is 0.86% of Ω_Λ — extraordinarily tight for a zero-parameter prediction.

4. The framework sharpens with better data: Unlike ΛCDM (where Λ is fit to data), this prediction becomes MORE constraining as σ(Ω_Λ) shrinks.

Honest Limitations

1. The “n=10 modes” argument relies on the heat kernel treating all metric components equally. Diffeomorphism gauge-fixing may reduce this.
2. The Higgs-graviton cancellation is coincidental, not structural. The framework doesn’t explain WHY it nearly cancels.
3. The cosmological parameter derivation assumes flat ΛCDM. If dark energy has w ≠ −1, the mapping changes.

Files

• src/graviton_precision.py: Core computation with exact arithmetic
• tests/test_graviton_precision.py: 10 tests, all passing
• run_experiment.py: Full 9-part analysis