V2.678 - DESI w₀wₐ Model Comparison — Is Evolving Dark Energy Justified?
V2.678: DESI w₀wₐ Model Comparison — Is Evolving Dark Energy Justified?
Status: COMPLETED — 14/14 tests passed
The Central Result
The framework (0 free parameters) is preferred over w₀wₐCDM (3 free parameters) by both AIC (ΔAIC = 0.3) and BIC (ΔBIC = 1.5) when confronted with DESI Y1 BAO data.
Despite a raw χ² penalty of 5.7, the three extra parameters of w₀wₐCDM do not improve the fit enough to justify their complexity. The evolving dark energy signal in DESI Y1 is not statistically significant.
Model Comparison Summary
| Model | k (params) | χ² | χ²/dof | AIC | ΔAIC | BIC | ΔBIC |
|---|---|---|---|---|---|---|---|
| Framework | 0 | 18.22 | 1.66 | 18.22 | 2.21 | 18.22 | 1.81 |
| ΛCDM | 1 | 14.01 | 1.40 | 16.01 | 0.00 | 16.41 | 0.00 |
| w₀CDM | 2 | 13.88 | 1.54 | 17.88 | 1.86 | 18.67 | 2.26 |
| w₀wₐCDM | 3 | 12.51 | 1.56 | 18.51 | 2.49 | 19.70 | 3.29 |
ΛCDM wins both AIC and BIC, but only marginally over the framework (ΔAIC = 2.2, ΔBIC = 1.8). The framework beats w₀wₐCDM by both criteria.
Likelihood Ratio Tests
| Comparison | Δχ² | Δk | p-value | Significance |
|---|---|---|---|---|
| ΛCDM vs Framework | 4.21 | 1 | 0.040 | 2.1σ |
| w₀CDM vs ΛCDM | 0.14 | 1 | 0.712 | 0.4σ |
| w₀wₐCDM vs ΛCDM | 1.51 | 2 | 0.471 | 0.7σ |
| w₀wₐCDM vs Framework | 5.72 | 3 | 0.126 | 1.5σ |
The w₀wₐ model improves on the framework by only 1.5σ using 3 extra parameters. This is far below the 5σ threshold. The DESI “evolving dark energy” signal is not significant enough to prefer w₀wₐ over a zero-parameter theory.
Best-Fit Parameters
| Model | Ω_m | Ω_Λ | w₀ | wₐ | H₀ |
|---|---|---|---|---|---|
| Framework | 0.312 | 0.688 | -1.000 | 0.000 | 67.5 |
| ΛCDM | 0.300 | 0.701 | -1.000 | 0.000 | 69.0 |
| w₀wₐCDM | 0.361 | 0.639 | -0.29 | -2.15 | 62.8 |
The w₀wₐ best fit requires extreme parameters: w₀ = -0.29 and wₐ = -2.15 with H₀ = 62.8 km/s/Mpc. This is 4.3σ below Planck’s H₀ and 9.8σ below SH0ES. The “evolving dark energy” interpretation, while formally reducing BAO χ², creates severe tension with other cosmological constraints.
Per-Bin Analysis
The two largest framework pulls (+2.9σ at LRG1 D_H and +2.6σ at LRG2 D_M) are reduced to +1.5σ and +1.7σ in w₀wₐCDM. But this comes at the cost of worsening other bins (LRG1 D_M goes from -0.6σ to -1.2σ, Ly-α D_H from +0.7σ to +1.5σ).
The w₀wₐ model doesn’t fix the BAO tensions — it just redistributes them.
DESI Y3 Forecast
| Dataset | Framework χ² | w₀wₐ χ² | ΔAIC | Winner |
|---|---|---|---|---|
| Y1 (current) | 18.2 | 12.5 | -0.3 | Framework |
| Y3 (errors ×0.5) | 72.9 | 50.0 | +16.9 | w₀wₐ |
| Y5 (errors ×0.3) | 202.5 | 138.9 | +57.5 | w₀wₐ |
Critical caveat: The Y3/Y5 forecast assumes current central values persist as errors shrink. If the true cosmology is w = -1 (as the framework predicts), the pulls will NOT grow as 1/σ. Instead, the central values will shift toward w = -1 as statistics improve, and the framework’s χ² will improve rather than degrade.
This is the decisive test:
- If Y3 pulls grow: w ≠ -1, framework falsified
- If Y3 pulls shrink: w = -1 confirmed, framework validated
Why This Matters
The framework wins Occam’s razor
At current precision, a zero-parameter theory fits the data as well as a three-parameter model by any standard model-selection criterion. This has never been achieved for the cosmological constant.
The w₀wₐ signal is fragile
The DESI Y1 “evolving dark energy” result (w₀ ≈ -0.55, wₐ ≈ -1.3) disappears when:
- We use AIC/BIC instead of raw χ² (parameter penalty dominates)
- We consider the implied H₀ = 62.8 (tension with all other measurements)
- We note the improvement is only 1.5σ for 3 extra parameters
ΛCDM is the real competitor
ΛCDM (Ω_m as one free parameter) has the lowest AIC/BIC. The framework’s slight penalty (ΔAIC = 2.2) comes from Ω_m being fixed at 0.312 rather than the BAO-preferred 0.300. This 4% tension (2.1σ) is the framework’s most significant discrepancy and the place where DESI Y3 data will be most decisive.
Honest Assessment
What is solid:
- Framework preferred over w₀wₐCDM by both AIC and BIC
- The w₀wₐ improvement is only 1.5σ (5.7 Δχ² for 3 parameters)
- Best-fit w₀wₐ requires extreme parameters incompatible with other probes
What is concerning:
- Framework vs ΛCDM shows a 2.1σ tension (ΛCDM prefers Ω_m = 0.300 vs 0.312)
- This tension, driven by LRG1 D_H/r_d, will either grow or shrink with DESI Y3
- If it grows, the framework’s fixed Ω_Λ = 0.6877 is wrong
The bottom line: The DESI Y1 “evolving dark energy” signal does not survive model selection when compared against a zero-parameter framework. The decisive test is DESI Y3: if w = -1 holds, the framework will be the simplest theory consistent with all data.