V2.343 - Framework vs w0waCDM — The DESI Confrontation
V2.343: Framework vs w0waCDM — The DESI Confrontation
Status: FRAMEWORK SURVIVES (BIC-preferred over w0waCDM with Bayes factor 8.3)
Objective
The framework predicts w = -1 exactly with ZERO free dark energy parameters. DESI (2024) hints at w0 != -1 (w0 ~ -0.85 in our fit). Does the DESI signal overcome the parameter penalty when comparing to the framework?
Method
Compared 4 models against 21 observations (CMB, DESI DR1 BAO, H0, SNe, growth):
| Model | DE params (k) | Description |
|---|---|---|
| Framework | 0 | Omega_L = 149*sqrt(pi)/384, w = -1 fixed |
| LCDM | 1 | Omega_L free, w = -1 fixed |
| w0CDM | 2 | Omega_L, w0 free, wa = 0 |
| w0waCDM | 3 | Omega_L, w0, wa all free (CPL) |
Model selection via AIC, BIC, and Bayes factors from BIC.
Key Results
Model comparison table
| Model | k | chi2 | AIC | BIC | Delta_BIC |
|---|---|---|---|---|---|
| Framework | 0 | 44.63 | 44.63 | 44.63 | 0.00 |
| LCDM | 1 | 42.89 | 44.89 | 45.94 | +1.31 |
| w0CDM | 2 | 40.54 | 44.54 | 46.63 | +2.00 |
| w0waCDM | 3 | 39.74 | 45.74 | 48.87 | +4.24 |
Framework has the lowest BIC. Best by AIC is w0CDM (by 0.09, negligible).
Bayes factors (BIC approximation)
| Comparison | Bayes Factor | Interpretation |
|---|---|---|
| Framework vs LCDM | 1.9 | Weak for framework |
| Framework vs w0CDM | 2.7 | Weak for framework |
| Framework vs w0waCDM | 8.3 | Substantial for framework |
| LCDM vs w0waCDM | 4.3 | Substantial for LCDM |
w0 != -1 not significant
- Delta_chi2(LCDM -> w0CDM) = 2.35 for 1 extra parameter (needs > 4.0)
- Delta_chi2(LCDM -> w0waCDM) = 3.15 for 2 extra parameters (needs > 6.2)
- Delta_chi2(Framework -> w0waCDM) = 4.89 for 3 extra parameters (needs > 8.0)
None of these improvements are statistically significant.
Best-fit w0waCDM parameters
- w0 = -0.85, wa = -0.45, Omega_L = 0.689
- Consistent with DESI 2024 findings but not significant over LCDM
Category chi2 breakdown
| Category | N | Framework | LCDM | w0waCDM |
|---|---|---|---|---|
| CMB | 2 | 0.28 | 2.05 | 0.64 |
| H0 | 2 | 1.84 | 1.19 | 1.62 |
| BAO | 12 | 18.23 | 16.13 | 13.51 |
| SNe | 2 | 6.96 | 8.61 | 7.44 |
| Growth | 3 | 17.32 | 14.91 | 16.53 |
Framework wins CMB and SNe categories; BAO drives the w0 != -1 preference (chi2 drops 18.23 -> 13.51 with 3 extra parameters), but the improvement is insufficient to overcome the BIC penalty.
What would kill the framework?
For w0waCDM to have lower BIC than framework:
- Need chi2(w0waCDM) < 35.50
- Currently: chi2(w0waCDM) = 39.74
- Gap: 4.24 in chi2
If DESI DR3 halves BAO errors while maintaining w0 ~ -0.85:
- Expected Delta_chi2 ~ 4x current ~ 20
- This would exceed the 3*ln(21) = 9.1 BIC penalty
- DESI DR3 is the decisive test
Significance
-
The framework survives its biggest current threat. Despite DESI hints at evolving dark energy, the zero-parameter prediction w = -1, Omega_L = 0.6877 remains BIC-preferred.
-
The parameter penalty is the framework’s shield. With k = 0 dark energy parameters, the framework gets no BIC penalty. w0waCDM must improve chi2 by > 9.1 to overcome its 3-parameter penalty.
-
DESI DR3 will be decisive. If w0 ~ -0.85 persists with halved errors, the chi2 improvement will likely exceed the BIC threshold, killing the framework. If w0 returns to -1.0, the framework becomes even more strongly preferred.
Caveats
- Simplified likelihood: We use diagonal chi2 (no covariance matrices between BAO measurements at different redshifts).
- Limited data: 21 observations; full Planck + DESI analysis uses thousands of data points with full covariance.
- Nelder-Mead fits: Global optimality not guaranteed for w0waCDM, but results are consistent with DESI published values.
Files
src/w0wa_comparison.py: CosmoModel with CPL dark energy, fitting, model selectionrun_experiment.py: 11-section analysis comparing 4 modelstests/test_w0wa.py: Unit tests (10 tests)