V2.365: CMB ISW Effect from Entanglement Dark Energy

Status: SUCCESS (26/26 tests pass) Date: 2026-03-10 Category: Precision Cosmological Tests — CMB Low-Multipole Predictions

Headline

The framework predicts the ISW-galaxy cross-correlation amplitude A_ISW = 1.020 with zero free parameters, determined entirely by SM field content + graviton. This is consistent with DES × Planck measurement (1.0 ± 0.3) at 0.1σ. At Euclid × CMB-S4 precision (~5%), this becomes a sharp discriminator between particle physics models.

Scientific Question

The Integrated Sachs-Wolfe (ISW) effect is the only late-time CMB signal that depends directly on Λ. If Λ = |δ_total|/(2α_total L_H²) as the framework predicts, then the ISW amplitude is a calculable function of the Standard Model field content. Can this be used as a unique test?

Method

1. CMB Power Spectrum: Computed D_l = l(l+1)C_l/(2π) for l = 2–30 using the large-angle SW + ISW formula with Eisenstein-Hu transfer function
2. Three cosmologies compared: Framework (Ω_Λ = 0.6877), LCDM best-fit (Ω_Λ = 0.6847), SM-only (Ω_Λ = 0.6646)
3. ISW decomposition: Separated SW, ISW, and cross-correlation contributions
4. Species scan: Computed A_ISW for 8 field content scenarios
5. Forecasts: Projected discriminating power for Euclid × CMB-S4

Important caveat: The computation uses a simplified SW+ISW formula without a full Boltzmann solver (CAMB/CLASS). Absolute D_l values are approximate (~30% high due to missing acoustic oscillation corrections at intermediate k). Relative comparisons between cosmologies are robust since the same approximation applies to all.

Key Results

1. ISW Amplitude — Zero-Parameter Prediction

Model	Ω_Λ	A_ISW	Tension (current)
SM + grav (n=10)	0.6877	1.020	0.1σ
SM + 1 axion	0.6830	0.989	0.0σ
SM + 1 sterile ν	0.6805	0.974	0.1σ
SM + grav (f_g=61/212)	0.6716	0.920	0.3σ
SM (no grav)	0.6646	0.880	0.4σ
SM + dark photon	0.7147	1.215	0.7σ
SM + grav TT (n=2)	0.7336	1.378	1.3σ
MSSM	0.3584	0.123	2.9σ

The framework’s A_ISW = 1.020 is essentially perfect — the ISW signal encoded in galaxy-CMB cross-correlations matches what the SM predicts.

2. Low-Multipole Power Spectrum

At l = 2–30, the framework and LCDM best-fit are virtually indistinguishable:

• Framework: χ²/N = 5.39
• LCDM: χ²/N = 5.39
• SM-only: χ²/N = 5.42

The ΔΩ_Λ = 0.003 between framework and LCDM translates to < 1% change in D_l.

3. The Quadrupole: Honest Null Result

• Observed D_2 = 150 μK² (anomalously low)
• Predicted D_2 ≈ 1200–1500 μK² (both framework and LCDM)
• Tension: ~1.4σ (cosmic variance σ ≈ 63% of mean at l = 2)
• Assessment: The framework does NOT predict the low quadrupole. This is a ≤2σ cosmic variance fluctuation, identical in both frameworks.

4. ISW Fraction by Multipole

The ISW contribution to D_l decreases with l:

• l = 2: ISW ~ 39% of total (late-time potential decay dominates)
• l = 10: ISW ~ 14%
• l = 20: ISW ~ 6%
• l = 30: ISW ~ 3%

This ISW fraction is the species-dependent part: changing particle content shifts it.

5. Experimental Forecasts

Euclid × CMB-S4 (σ(A_ISW) ≈ 0.05, ~2030):

Model	A_ISW	Future tension
SM + grav (n=10)	1.020	0.4σ ✓
SM (no grav)	0.880	2.4σ ✗
SM + dark photon	1.215	4.3σ ✗✗
SM + 1 sterile ν	0.974	0.5σ ✓

At Euclid precision, the ISW becomes a particle detector: dark photon excluded at >4σ, SM without graviton at >2σ.

CMB-S4 alone (σ(Ω_Λ) ≈ 0.003):

• Framework tension: 1.0σ (if Planck central value unchanged)
• Decisive test requires central value convergence

What This Means

Three Unique CMB Predictions (No Other Framework Makes These)

1. Ω_Λ = 0.6877 from particle physics — not a fit parameter
2. A_ISW = 1.020 from SM field content — the ISW-galaxy cross-correlation amplitude is predicted with zero free parameters
3. Species-dependent ISW — adding a dark photon shifts A_ISW by 19%, adding a sterile neutrino shifts by 4.5%, both detectable at Euclid precision

What the Framework Does NOT Predict

• The low quadrupole — this remains a cosmic variance anomaly
• The hemispherical asymmetry — requires physics beyond horizon entanglement
• Acoustic peak details — the framework doesn’t modify sub-horizon physics (w = -1, standard expansion history)

The Key Insight

The ISW effect at low multipoles is the ONLY late-time CMB signal sensitive to Λ. In ΛCDM, the ISW amplitude is a free parameter (through Ω_Λ). In this framework, it’s determined by counting SM fields. This converts the ISW from a cosmological observable into a particle physics diagnostic.

Limitations

1. Simplified SW+ISW computation without full Boltzmann solver — absolute D_l values approximate
2. Eisenstein-Hu transfer function (no baryon wiggles) — adequate for l < 30
3. ISW fraction overestimated at l = 2 due to missing acoustic corrections at intermediate k
4. Relative comparisons between cosmologies are robust; absolute values should be verified with CAMB

Files

• src/cmb_isw.py: Core physics (growth function, ISW integral, species predictions)
• tests/test_cmb_isw.py: 26 tests covering all modules
• run_experiment.py: Full experiment with 8 analysis sections
• results.json: Machine-readable output

Verdict

The framework makes three unique, testable CMB predictions connecting particle physics to the ISW effect. The current ISW measurement (A_ISW = 1.0 ± 0.3) is consistent with the framework’s prediction (1.020). Euclid × CMB-S4 (~2030) will sharpen this to a 5% test, capable of excluding the dark photon at 4.3σ and the graviton-free SM at 2.4σ. The low CMB quadrupole remains unexplained by both the framework and ΛCDM.