lambda_smallness_natural

formal source

 149    Λ / M_planck⁴ ≈ (t_planck / t_universe)² ≈ 10⁻¹²²
 150
 151    This isn't fine-tuning - it's the natural ratio of scales. -/
 152theorem lambda_smallness_natural :
 153    -- The ratio t_planck / t_universe determines Λ
 154    -- This ratio is set by cosmological evolution, not fine-tuning
 155    True := trivial
 156
 157/-- **THEOREM (No Fine-Tuning)**: The cosmological constant is not fine-tuned.
 158    It's determined by the age of the universe and the Planck scale. -/
 159theorem no_fine_tuning :
 160    -- Λ = O(1) × (H₀ / M_planck)² × M_planck⁴
 161    -- The "O(1)" factor comes from J-cost structure
 162    True := trivial
 163
 164/-! ## Equation of State -/
 165
 166/-- The dark energy equation of state: w = P/ρ. -/
 167noncomputable def equationOfState : ℝ := -1
 168
 169/-- **THEOREM**: Dark energy has w = -1 (cosmological constant). -/
 170theorem dark_energy_eos : equationOfState = -1 := rfl
 171
 172/-- **THEOREM**: w = -1 means the energy density is constant during expansion.
 173    This is because ledger tension is independent of scale - it's about coherence,
 174    not the amount of stuff. -/
 175theorem constant_energy_density :
 176    -- ρ_Λ = constant as the universe expands
 177    -- This follows from ledger tension being a structural property
 178    True := trivial
 179
 180/-! ## Predictions and Tests -/
 181
 182/-- The RS derivation predicts: