rsPredictions
RS dark energy predictions fix the equation of state at w = -1 with Lambda scaling as H0 squared and an emergent ledger-tension origin. Cosmologists testing Recognition Science against supernova and CMB data would reference this record. The definition simply packages the values obtained from the ledger-balance constraint under expansion.
claimThe Recognition Science model predicts dark energy with equation of state parameter $w = -1$, scaling relation $Lambda propto H_0^2$, and emergent nature from ledger tension during cosmic expansion.
background
In the COS-006 module dark energy arises as residual J-cost when the global ledger balance requirement meets the creation of new spacetime volume during expansion. The DarkEnergyPredictions structure records three quantities: the equation of state w, the lambda_scaling string, and a nature descriptor. Upstream results include the ledger factorization from DAlembert and the phi-forcing structure that calibrate J.
proof idea
The definition constructs the DarkEnergyPredictions record directly with the three fields set to the ledger-tension values. No lemmas are applied beyond the structure definition itself.
why it matters in Recognition Science
This definition supplies the concrete predictions that downstream modules such as Inflation.rsPredictions and QuantumErrorCorrection.rsPredictions incorporate when building their own forecast lists. It fills the COS-006 derivation step in the Recognition Science chain, linking ledger tension to the observed accelerating expansion without invoking a fundamental cosmological constant. The framework landmark here is the global J-cost sum to zero under expansion, yielding the small Lambda value.
scope and limits
- Does not compute a numerical value for the Hubble constant.
- Does not simulate the time evolution of dark energy density.
- Does not address quantum corrections to the ledger tension.
- Does not compare against specific observational datasets.
formal statement (Lean)
196def rsPredictions : DarkEnergyPredictions := {
proof body
Definition body.
197 w := -1,
198 lambda_scaling := "Λ ∝ H₀²",
199 nature := "Emergent from ledger tension during cosmic expansion"
200}
201
202/-! ## Falsification Criteria -/
203
204/-- The dark energy derivation would be falsified by:
205 1. Measured w ≠ -1 (significantly)
206 2. Λ varying with cosmic epoch in ways not matching H₀² scaling
207 3. Discovery of fifth force at cosmological scales
208 4. Dark energy "clumping" (it should be perfectly uniform) -/