V2.409 - Cosmological Parameters from Lambda — The Framework's H_0 Prediction
V2.409: Cosmological Parameters from Lambda — The Framework’s H_0 Prediction
Key Result
The framework predicts Omega_Lambda = 0.6877 with zero free parameters. Combined with the CMB acoustic scale theta_*, this predicts H_0:
| Parameter | Framework | Planck LCDM | Difference |
|---|---|---|---|
| H_0 (km/s/Mpc) | 67.63 | 67.36 ± 0.54 | +0.27 |
| Omega_Lambda | 0.6877 (predicted) | 0.6847 (fit) | +0.003 |
| Omega_M | 0.3122 | 0.3152 | −0.003 |
| t_0 (Gyr) | 13.78 | 13.80 | −0.02 |
| w | −1 (exact) | −1 (assumed) | — |
The framework has one fewer free parameter than LCDM (5 vs 6): Omega_Lambda is predicted, not fit, and H_0 becomes a derived quantity.
The Hubble Tension Verdict
- Framework predicts H_0 = 67.63 km/s/Mpc (+0.5σ from Planck)
- SH0ES measures H_0 = 73.04 ± 1.04 km/s/Mpc
- Framework vs SH0ES: −5.2σ tension
- The +0.27 km/s/Mpc shift is in the right direction but covers only 4.7% of the 5.7 km/s/Mpc gap
The framework does NOT resolve the Hubble tension. It predicts w = −1 exactly, giving standard late-time expansion. Reaching H_0 = 73 would require Omega_Lambda ≈ 0.749 — 9σ from the framework prediction.
This is honest and expected: the framework is a theory of Lambda, not a resolution of the Hubble tension. If the tension is real, both the framework and LCDM need additional physics (early dark energy, modified gravity, etc.).
Key Derivative: dH_0/dOmega_Lambda
The gradient dH_0/dOmega_Lambda ≈ 88.7 km/s/Mpc per unit Omega_Lambda. This means:
- Euclid (σ = 0.002): H_0 uncertainty contribution ≈ 0.18 km/s/Mpc
- Each BSM particle shifts H_0 by a calculable amount (via Omega_Lambda)
- +1 vector (Z’): ΔH_0 ≈ +2.7 km/s/Mpc → immediately testable
Method
We use a calibrated solver: compute the SHIFT in H_0 when changing Omega_Lambda from Planck’s 0.6847 to the framework’s 0.6877, using a simplified Friedmann equation solver with numerical sound horizon integration. The relative shift is robust (independent of the sound horizon systematic). Absolute H_0 calibrated to Planck’s 67.36 km/s/Mpc.
Future Tests
| Experiment | Precision | Can it test? |
|---|---|---|
| DESI DR2 (2025) | σ(H_0) ~ 1.5 | Yes — H_0 = 67.6 ± 1.5 |
| Euclid (2025-2030) | σ(Ω_Λ) = 0.002 | Yes — framework at +1.4σ |
| CMB-S4 (~2030) | tightens θ_* | Tightens H_0 further |
| Einstein Telescope (~2035) | σ(H_0) = 0.1 | Decisive: 3σ between framework (67.6) and Planck (67.4) |
What’s New
- H_0 as a prediction: In LCDM, H_0 is fit to data. Here it’s derived: H_0 = 67.63 km/s/Mpc.
- One fewer free parameter: The framework eliminates Omega_Lambda as a free parameter, reducing from 6 to 5 cosmological parameters.
- Hubble tension position: The framework is firmly on the CMB side. If SH0ES is right, the framework is falsified (−5.2σ) — but so is LCDM.
- dH_0/dOmega_Lambda = 88.7: Each BSM particle that shifts Omega_Lambda also shifts H_0 by a calculable amount. A single Z’ would push H_0 to ~70 km/s/Mpc.
Caveats
- H_0 shift computed via calibrated simplified solver; full CAMB/CLASS would refine the absolute value
- The +0.27 km/s/Mpc shift is small — the framework essentially agrees with Planck
- The framework cannot accommodate the Hubble tension (w = −1 exactly)
- If DESI confirms w ≠ −1, the entire framework is falsified regardless of H_0