V2.344: Framework vs w₀wₐCDM — The DESI Confrontation

Purpose

Extend V2.341’s Bayesian comparison from ΛCDM (1 param) to w₀wₐCDM (3 params). DESI DR2 reports (w₀, wₐ) ≈ (−0.73, −1.05), which is 4.1σ from the framework’s prediction of (−1, 0). But w₀wₐCDM fits 2 extra parameters. Does the Occam penalty offset the tension?

Method

Savage-Dickey density ratio in the 2D (w₀, wₐ) plane with a bivariate Gaussian posterior (σ_w₀ = 0.067, σ_wₐ = 0.31, ρ = −0.85 from DESI DR2+CMB+SNe).

Key Results

1. The DESI Tension

	Framework	DESI DR2
w₀	−1.000	−0.727 ± 0.067
wₐ	0.000	−1.05 ± 0.31

Mahalanobis distance: 4.08σ (χ² = 16.62). This is serious.

2. Occam Decomposition

Factor	Value	Meaning
Fit factor	exp(−χ²/2) = 0.0002	Framework is 4,072× worse than best fit
Occam factor	0.0017	w₀wₐCDM uses only 0.17% of prior volume
Net B(w₀wₐ)	0.14	w₀wₐCDM preferred

The Occam penalty for 2 extra parameters is strong (582×), but the 4.1σ fit penalty is stronger (4,072×). The DESI tension wins.

3. Three-Way Comparison

Comparison	log₁₀(B)	Interpretation
Framework vs ΛCDM (Ω_Λ only)	+1.70	Very strong for framework
ΛCDM vs w₀wₐCDM (w₀,wₐ only)	−0.84	w₀wₐCDM preferred
Framework vs w₀wₐCDM (all)	+0.85	Substantial for framework

The framework survives the DESI confrontation with B = 7 overall, but only because the Ω_Λ prediction (B = 50) compensates for the w₀wₐ loss (B = 0.14).

4. Prior Sensitivity

Prior	w₀ range	wₐ range	log₁₀(B)
Tight	[−2, 0]	[−2, 2]	−1.54
Moderate	[−3, 1]	[−5, 5]	−0.84
Wide	[−5, 3]	[−10, 10]	−0.24
Very wide	[−10, 10]	[−20, 20]	+0.46

With a “very wide” prior, the framework is marginally preferred even for (w₀, wₐ) alone. With any reasonable physical prior, w₀wₐCDM is preferred on equation of state.

5. Future DESI Scenarios (σ_w₀ → 0.04, σ_wₐ → 0.15)

Scenario	(w₀, wₐ)	Tension	log₁₀(B)
A: Converges to w = −1	(−0.95, −0.10)	1.5σ	+2.84 (Decisive)
B: Stays at DESI DR2	(−0.73, −1.05)	7.2σ	−7.94 (Falsified)
C: Intermediate	(−0.90, −0.30)	2.5σ	+1.93 (Very strong)

This is the decisive test. If DESI hardens at w₀ ≈ −0.7, the framework is falsified at ~8σ equivalent. If DESI drifts toward w = −1, the framework wins decisively.

Interpretation

The honest picture

1. The framework currently survives the DESI confrontation, but only because its spectacular Ω_Λ prediction (B = 50) compensates for the w₀wₐ tension (B = 0.14).

2. Combined: B = 7 (log₁₀ = 0.85, “Substantial”). The framework is still the better bet, but it’s no longer comfortable.

3. The DESI tension is real and cannot be dismissed. At 4.1σ in the (w₀, wₐ) plane, it is the framework’s most serious observational challenge.

4. The Occam argument is NOT enough to save the framework from the DESI equation-of-state data alone. The 2-parameter Occam penalty (582×) is overwhelmed by the fit penalty (4,072×).

5. DESI DR3+ is existential. If central values stay and errors shrink by 2×, the framework is falsified. If central values drift 1σ toward (−1, 0), the framework wins decisively.

What this means for the framework

The framework makes an absolute prediction: w = −1, dw/da = 0, forever. This is the strongest possible statement — and the most falsifiable. The DESI data is the first real test of this prediction, and the result is uncomfortable but not fatal.

The framework’s survival strategy is not to explain away the DESI tension but to let the data decide. If w truly evolves, the framework is wrong — and that would be the most interesting possible outcome, because it would mean the cosmological constant is NOT explained by entanglement entropy.

Files

• src/w0wa_confrontation.py — Savage-Dickey 2D, Occam decomposition, scenarios, combined analysis
• tests/test_w0wa.py — 14 tests, all passing
• run_experiment.py — Full analysis (8 sections)
• results.json — Machine-readable results

Status

COMPLETE — Framework survives DESI confrontation (B = 7 overall) but loses on equation-of-state alone (B = 0.14). DESI DR3+ is existential.