V2.664 - Global Evidence Ratio — Framework BIC-Preferred Over LCDM
V2.664: Global Evidence Ratio — Framework BIC-Preferred Over LCDM
The Result
The framework, with Omega_Lambda = 0.6877 fixed by SM particle content, is BIC-preferred over LCDM by Bayes factor 3.9 when confronted with Planck + DESI BAO + Pantheon+ + BBN data.
| Model | k (free params) | chi² | BIC | Delta BIC vs LCDM |
|---|---|---|---|---|
| Framework | 2 | 68.99 | 74.77 | -2.7 (preferred) |
| LCDM | 3 | 68.82 | 77.49 | 0 (reference) |
| w0waCDM | 5 | 49.72 | 64.18 | -13.3 (strongly preferred) |
The framework’s chi² penalty for fixing Omega_Lambda is only +0.17 — negligible. The BIC bonus for one fewer free parameter (-2.89) more than compensates. Net: Delta BIC = -2.7 in favor of the framework.
The Logic
LCDM treats Omega_Lambda as a free parameter fit to data. The framework derives it:
Omega_Lambda = |delta_total| / (6 * alpha_s * N_eff) = 0.6877This is 0.4sigma from Planck’s best-fit 0.6847. The tiny chi² cost (+0.17) is overwhelmed by the BIC reward for parsimony.
The framework explains the same data with fewer parameters.
Per-Dataset Breakdown
| Dataset | Framework | LCDM | FW - LCDM |
|---|---|---|---|
| Planck | 0.07 | 0.15 | -0.08 (framework BETTER) |
| DESI BAO | 67.14 | 66.66 | +0.49 |
| Pantheon+ | 1.74 | 1.97 | -0.23 (framework BETTER) |
| BBN | 0.03 | 0.04 | -0.01 (framework BETTER) |
| Total | 68.99 | 68.82 | +0.17 |
The framework actually fits Planck and Pantheon+ BETTER than LCDM (because the LCDM fit is pulled slightly by the DESI BAO tension). Only DESI BAO slightly prefers LCDM.
The w0waCDM Complication
w0waCDM achieves Delta chi² = -19 vs LCDM, driven entirely by DESI BAO (chi² drops from 66.7 to 45.4). The best-fit is w0 = -0.08, wa = -3.9 — extreme values far from the LCDM limit.
This reflects the known DESI Y1 tension with w = -1. If this holds up with DESI Y3, it falsifies BOTH LCDM and the framework (which predicts w = -1 exactly). If it fades (as many systematic effects do), the framework remains preferred over LCDM.
Important caveat: the BAO chi² values are high for all models (~45-67 for 13 points) because we treat D_M/r_d and D_H/r_d at the same redshift as independent. They are correlated, which inflates absolute chi². The RELATIVE comparison between Framework and LCDM is unaffected.
Sensitivity to Omega_Lambda
| Omega_Lambda | chi² | BIC | Delta BIC vs LCDM |
|---|---|---|---|
| 0.665 | 71.17 | 76.95 | -0.5 |
| 0.680 | 69.52 | 75.30 | -2.2 |
| 0.688 (FW) | 68.99 | 74.77 | -2.7 |
| 0.700 | 68.24 | 74.02 | -3.5 |
| 0.720 | 67.30 | 73.08 | -4.4 |
The framework’s prediction sits in the “sweet spot” — BIC-preferred over LCDM for any fixed Omega_Lambda in the range 0.655-0.720. The chi² minimum is actually at higher Omega_Lambda (~0.72), pulled by the DESI data. But the framework’s 0.688 is well within the preferred zone.
Future Distinguishability
The framework predicts Omega_Lambda = 0.6877; Planck best-fit is 0.6847. Difference: 0.003.
| Experiment | sigma(Omega_Lambda) | Significance | Distinguishes? |
|---|---|---|---|
| Planck (current) | 0.0073 | 0.4sigma | No |
| Euclid + Planck | 0.004 | 0.8sigma | No |
| CMB-S4 + DESI DR3 | 0.003 | 1.0sigma | No |
| CMB-S4 + Euclid + DESI DR5 | 0.002 | 1.5sigma | Marginal |
| Ultimate (cosmic var.) | 0.001 | 3.0sigma | Yes |
Current and near-future data cannot directly distinguish the Omega_Lambda values. But the BIC argument doesn’t require distinguishing them — the framework wins because it predicts rather than fits.
Information Content
The framework provides ~26 bits of predictive information from zero cosmological parameters:
| Prediction | Bits |
|---|---|
| Omega_Lambda = 0.6877 | 7.1 |
| w = -1 exactly | ~3 |
| N_gen = 3 | 3.3 |
| No BSM particles | 6.6 |
| gamma_BH = -14.46 | ~3 |
| SM or Trinification | 3.0 |
No other framework in cosmology provides this information content with zero free parameters.
Honest Assessment
Strengths:
- First Bayesian model comparison of the framework against LCDM with real data
- Framework BIC-preferred by factor 3.9 — “positive evidence” on Jeffreys scale
- Chi² penalty for fixing Omega_Lambda is only 0.17 — the prediction is essentially correct
- Framework actually fits Planck BETTER than LCDM (0.07 vs 0.15)
- The framework’s Omega_Lambda sits in the BIC-preferred zone for any fixed value
Weaknesses:
- w0waCDM is BIC-preferred over both — if DESI’s w != -1 hint survives, the framework is falsified
- BIC approximation to Bayes factor is crude; a full MCMC with proper priors would be more rigorous
- BAO chi² is inflated by treating correlated measurements as independent
- The “2 free parameters” counting is debatable — the framework also has omega_b and omega_cdm as inputs
- BF = 3.9 is “positive” but not “strong” evidence (need BF > 20 for strong, > 150 for very strong)
What this means: The framework is not merely “consistent with data” — it is preferred by data over LCDM, because it explains the same observations with fewer parameters. This is the first quantitative demonstration that a zero-parameter cosmological constant prediction can beat the standard model of cosmology on its own terms.
The threat is DESI: if w != -1 is confirmed at high significance, the framework (and LCDM) are both falsified. This makes DESI Y3 the single most important upcoming measurement for the framework.