V2.520: Multi-Probe Stress Test — Ω_Λ = 0.6877 vs All Cosmological Data

Status: STRONG RESULT — Zero-parameter prediction survives 82 measurements

Key Finding

The framework’s zero-parameter prediction Ω_Λ = 0.6877 is confronted with 82 independent measurements across 11 cosmological probes spanning 11 decades in redshift (z = 0.01 to z = 10⁹). The core fit gives χ²/dof = 1.07 with zero free parameters. The prediction adds no new tensions beyond those already present in ΛCDM.

Global Fit Statistics

Dataset	χ²	dof	χ²/dof
ALL measurements	134.9	82	1.65
Excluding local H₀	89.5	78	1.15
Core (excl H₀ + A_L)	81.7	76	1.07

• 90% of measurements within 2σ (74/82)
• 98% of measurements within 3σ (80/82)
• Only 2 measurements beyond 3σ: SH0ES H₀ (+5.3σ) and H0LiCOW H₀ (+3.2σ)

Probe-by-Probe Results

| Probe | N | χ²/N | Max |σ| | Verdict | |-------|---|------|---------|---------| | CMB (shift parameter) | 2 | 0.10 | 0.5σ | PASS | | BAO (DESI Y1 + SDSS) | 15 | 1.30 | 2.8σ | PASS | | Cosmic chronometers | 32 | 0.47 | 1.6σ | PASS | | Type Ia SNe (Pantheon+) | 19 | 1.37 | 1.9σ | PASS | | BBN (Y_p + D/H) | 2 | 0.36 | 0.7σ | PASS | | Age of universe | 2 | 0.94 | 1.2σ | PASS | | Transition redshift | 1 | 0.09 | 0.3σ | PASS | | Weak lensing (S₈) | 3 | 6.10 | 2.9σ | TENSION* | | CMB lensing (A_L) | 2 | 3.89 | 2.8σ | TENSION* | | Local H₀ (SH0ES/TRGB) | 2 | 15.22 | 5.3σ | TENSION* | | Strong lensing | 2 | 7.52 | 3.2σ | TENSION* |

*All starred tensions are pre-existing ΛCDM tensions, not new failures of the framework.

What This Means

7 clean passes (χ²/N < 1.5)

The framework correctly predicts:

• CMB: Shift parameter R within 0.5σ
• BAO: 15 distance measurements from z = 0.1 to z = 2.3 (DESI + SDSS)
• Cosmic chronometers: 32 direct H(z) measurements from differential galaxy aging
• Type Ia supernovae: 19 binned distance moduli from Pantheon+
• BBN: Helium-4 (Y_p) and deuterium (D/H) abundances at z ~ 10⁹
• Age: Consistent with both Planck age and globular cluster ages
• Transition redshift: z_T = 0.64 (deceleration → acceleration) matches data

4 inherited tensions

The framework predicts H₀ = 67.5 km/s/Mpc (Planck side). This means:

• SH0ES (+5.3σ): The Hubble tension. Framework falsified if SH0ES is correct.
• Weak lensing (~−2.9σ): The S₈ tension. Framework gives S₈ = 0.825, lensing measures ~0.77.
• Planck A_L (+2.8σ): The lensing anomaly. Framework predicts A_L = 1.
• These tensions exist in ΛCDM too — the framework neither creates nor resolves them.

Bayesian Comparison: Framework vs ΛCDM

• Framework: 0 free cosmological parameters
• ΛCDM: 1 free parameter (Ω_Λ)
• Ω_Λ shift: 0.6877 vs best-fit 0.6847 = +0.42σ

The Occam factor for having zero parameters gives ln(O) = 4.0. The framework wins the Bayesian comparison unless the best-fit ΛCDM improves χ² by more than 8.0 — but with only a 0.42σ shift in Ω_Λ, the actual improvement is ~0.2. The framework is strongly Bayesian-preferred over ΛCDM.

Honest Assessment

Strengths

1. χ²/dof = 1.07 with zero parameters is remarkable. Most cosmological models achieve this only with several free parameters.
2. 11 decades in redshift: The same prediction works from BBN (z ~ 10⁹) through recombination (z ~ 1100) to today (z ~ 0). This is not fine-tuning.
3. No new tensions: Every failure point is a known ΛCDM tension. The framework doesn’t make things worse anywhere.
4. Cosmic chronometers (32 measurements, χ²/N = 0.47): An independent probe not previously tested against the framework. Clean pass.

Caveats

1. Approximate SNe data: The Pantheon+ binned distance moduli used here are approximate (not the official compressed likelihood). A proper analysis with full covariance matrices could change the SNe chi².
2. r_d from fitting formula: The sound horizon uses the Aubourg et al. (2015) fitting formula (0.1% accuracy). Full Boltzmann code (CAMB/CLASS) would be needed for sub-percent precision.
3. Hubble tension is existential: If SH0ES H₀ = 73.0 is confirmed as the true value, the framework is ruled out at >5σ. The TRGB measurement (69.8 ± 1.7) gives only 1.4σ tension — the resolution of the Hubble tension is critical for the framework’s viability.
4. BAO D_H at z = 0.51: The 2.8σ tension in D_H/r_d for DESI LRG1 is worth monitoring. It suggests H(z=0.51) may be slightly lower than predicted.

Connection to Other Experiments

• V2.516: Zero-parameter expansion history (7 derived quantities) — this experiment extends to 82 measurements
• V2.517: Vacuum energy vs trace anomaly (the theoretical foundation for why Ω_Λ works)
• V2.519: DESI Y1 confrontation (BAO subset of this analysis)
• V2.457: Bayesian evidence (proper evidence calculation with fewer probes)
• V2.512: Predictive information content (information-theoretic perspective)

Files

• src/multi_probe.py: Core module with cosmological calculations and data compilation
• tests/test_multi_probe.py: 13 tests (all passing)
• run_experiment.py: Full 9-section analysis
• results.json: Machine-readable results