V2.426: CMB Quadrupole Suppression from Horizon Entanglement

Date: 2026-03-11 Group: 7-cosmological-prediction Status: COMPLETE — qualitative consistency, NOT a quantitative prediction

Objective

Investigate whether the framework’s horizon entanglement structure can explain the anomalously low CMB quadrupole (l=2): observed D₂ ≈ 174 μK² vs ΛCDM prediction ≈ 1110 μK², an 84% deficit at 2.0σ.

The Anomaly

Quantity	Value
D₂ observed (Planck 2018)	173.6 μK²
D₂ predicted (ΛCDM)	1110.2 μK²
Ratio	0.156 (15.6%)
P(D₂ ≤ obs | ΛCDM)	2.18%
Tension	2.0σ

Framework Suppression Models

Zero-Parameter Models (from R = |δ|/(6α) = 0.688 only)

Model	f₂ (suppression)	D₂ predicted	χ² (l=2–10)	vs ΛCDM
ΛCDM (baseline)	1.000	1110 μK²	76.2	—
R/l(l+1)	0.885	983 μK²	57.6	×1.3 better
Entanglement fraction	0.725	805 μK²	35.9	×2.1 better

Tuned Models (free parameters)

Model	f₂	D₂ predicted	χ² (l=2–10)	Parameters
Best-fit exponential	0.240	267 μK²	5.5	l_H=4.67, A=1.0

Key Findings

1. Direction is correct

Both zero-parameter models predict D₂ lower than ΛCDM, consistent with the observed deficit. The entanglement fraction model (f₂ = 0.725) improves the χ² by a factor 2.1× over ΛCDM across l=2–10.

2. Magnitude is insufficient

The framework’s parameter R ≈ 0.69 gives at most ~28% suppression at l=2 (entanglement fraction model), but the observed deficit is 84%. The framework is too weak by a factor ~3–5.

3. No parameter-free quadrupole prediction

The best-fit exponential (l_H = 4.67) achieves good fit but has 2 free parameters, and l_H does not map to any framework quantity:

• √(6R) = 2.03 ≠ 4.67
• 1/R = 1.45 ≠ 4.67
• π/√R = 3.79 ≠ 4.67

4. Cosmic variance is large at l=2

With only 5 degrees of freedom, the cosmic variance at l=2 is ~45%. Even ΛCDM’s P = 2.2% is not highly anomalous. The framework models increase this to P = 2.9% (R/l²) and P = 4.4% (entanglement fraction) — modest improvements.

Honest Assessment

This is NOT a unique testable prediction of the framework. The CMB quadrupole anomaly is:

• Only 2.0σ in ΛCDM (could be a fluctuation)
• Not quantitatively predicted by the framework without free parameters
• The suppression mechanism is qualitative (entanglement → reduced power) without a rigorous derivation connecting S = αA + δ ln(A) to the primordial power spectrum

What this DOES establish:

• The framework has the right qualitative structure to suppress low-l modes
• The parameter R naturally sets a horizon-scale suppression
• If a rigorous derivation were possible, connecting trace anomaly to CMB power spectrum modifications, this COULD become a prediction

Strategic conclusion: The CMB quadrupole is NOT the right smoking gun for this framework. The framework’s strongest unique predictions remain:

1. ΔΛ = 0 through phase transitions (V2.423) — structurally unique
2. Species-dependence curve (V2.422) — falsifiable by particle discovery
3. BH entropy log coefficient (V2.348/404) — distinguishes from LQG
4. N_ν = 3 required (V2.326/328) — connects particle physics to Λ

Files

• src/cmb_quadrupole.py — Suppression models and CMB data
• tests/test_cmb_quadrupole.py — 9 tests, all passing
• run_experiment.py — Full analysis pipeline
• results.json — Machine-readable output