H0
The definition supplies the numerical value of the present-day Hubble parameter in natural units for Recognition Science cosmology calculations. Cosmologists working within the ledger-tension model cite it when deriving the cosmological constant from expansion-induced J-cost deficits. The declaration is a direct constant assignment with no proof obligations.
claim$H_0 := 2.2 × 10^{-18}$ in natural units with $c = 1$.
background
Recognition Science derives dark energy from ledger tension during cosmic expansion. The J-cost function measures recognition imbalance for each ledger entry, and the global ledger must sum to zero. Expansion creates new spacetime volume that requires additional entries, leaving a residual energy density identified with the cosmological constant.
proof idea
The declaration is a direct noncomputable definition assigning the observed Hubble scale. No lemmas are applied; it serves as a numerical anchor for downstream algebraic derivations of the tension energy density.
why it matters in Recognition Science
This value anchors the derivation of the cosmological constant as three times H0 squared, which downstream theorems prove positive and link to the phi-ladder via the J-cost per unit volume. It connects the eight-tick octave structure to observable cosmology, closing the loop from the recognition forcing chain to accelerating expansion.
scope and limits
- Does not derive the numerical value from the recognition forcing chain.
- Does not incorporate the phi-based expression for the Hubble parameter from the unification module.
- Does not model the time evolution of the expansion rate.
- Does not address observational uncertainties in the Hubble constant.
Lean usage
theorem lambda_pos : cosmologicalConstant > 0 := by unfold cosmologicalConstant H0; norm_numformal statement (Lean)
54noncomputable def H0 : ℝ := 2.2e-18
proof body
Definition body.
55
56/-- The Planck time (in seconds). -/