Evidence & Predictions
What the model predicts, how confident we are in each prediction, and what would kill it. For the derivations behind these numbers, see the Framework page.
Current Evidence
| Observable | ΛCDM says | We predict | Data shows | Status |
|---|---|---|---|---|
| σ₈ (clustering amplitude) | 0.811 | ≈ 0.76 ± 0.03 | 0.76–0.79 | Consistent |
| S₈ (weak lensing) | 0.83 | ≈ 0.78 ± 0.03 | 0.76–0.79 | Consistent |
| Lyman-α k-cutoff | none | k_c ≈ 0.75 h/Mpc | suppression observed | Consistent |
| G_eff during leakage | G_N | ≈ 0.75 G_N | consistent | Consistent |
| CMB acoustic peaks | fit | unchanged | Planck fit | Consistent |
| Damping-tail suppression | 0% | 1–3% | pending CMB-S4 | Pending |
Predictions by Confidence Tier
- • Effective gravity is transiently suppressed near z ≈ 50,000.
- • Small-scale power is suppressed relative to ΛCDM.
- • CMB acoustic peaks preserved.
These follow directly from the derived Bricks 1–3 and are the most robust part of the framework.
- • Power-spectrum cutoff at k_c ≈ 0.75 h/Mpc.
- • S₈ ≈ 0.78 ± 0.03.
- • Damping-tail suppression of 1–3%.
Requires the phenomenological Brick 4 mapping to hold; validated only if Boltzmann code reproduces σ₈.
- • σ₈ = 0.76 ± 0.03.
- • Radion equilibrium r₀ ≈ 0.75.
- • Potential steepness β ≈ 8.5.
Parameters are currently fitted with zero degrees of freedom; Stage 3 must derive them from first principles.
Falsification Criteria
- ◇ Precise linear P(k) at k ≈ 0.5–1 h/Mpc shows standard ΛCDM with no cutoff.
- ◇ σ₈ measured higher than ΛCDM (wrong sign of the effect).
- ◇ Lyman-α forest shows no small-scale suppression.
- ◇ Growth rate f(z) matches ΛCDM exactly.
- ◇ CMB damping-tail suppression > 5% (too large).
- ◇ PIXIE-class spectral-distortion measurement rules out any H(z) deviation near z ≈ 50,000.
All are testable within 2–3 years.
Four-Stage Validation Roadmap
- 1August 2026ActiveStage 1: Boltzmann code validation
Patch CAMB/CLASS with modified G_eff(z). Run with fixed parameters, extract σ₈, verify against target 0.76.
- 22027Stage 2: Alternative-model comparison
Show the leakage mechanism is distinguishable from Warm Dark Matter, Fuzzy Dark Matter, and other small-scale suppressors.
- 32027–2028Stage 3: First-principles 5D derivation
Derive Brick 4 (scale selection) from the 5D Einstein–Gauss-Bonnet equations rather than fitting.
- 42028–2029Stage 4: Observational tests
DESI, Euclid, Roman, and CMB-S4 measurements of P(k), growth rate, and damping tail.
Future Tests (2027–2029)
- • CMB-S4: 1–3% damping-tail suppression prediction.
- • Euclid: weak-lensing S₈ to 1% precision.
- • DESI Lyman-α: k_c cutoff extraction from the forest.
- • Roman: high-z galaxy-cluster growth history.