inflation_rs_synthesis

formal source

 212    3. Together: Inflation is J-cost driven toward Ω = 1
 213
 214    The inflaton potential is constrained by J-cost optimization. -/
 215def inflation_rs_synthesis : List String := [
 216  "Inflation provides the dynamics",
 217  "RS provides the target (Ω = 1)",
 218  "J-cost shapes the inflaton potential",
 219  "Exit from inflation at exactly Ω = 1"
 220]
 221
 222/-! ## Implications -/
 223
 224/-- If RS is correct about flatness:
 225
 226    1. **Cosmological constant**: Must have specific value (ρ_Λ/ρ_c ~ 0.7)
 227    2. **Dark matter**: Must exist to achieve Ω = 1
 228    3. **Future**: Universe expands forever (flat geometry)
 229    4. **Origin**: Ledger geometry determines spacetime geometry -/
 230def implications : List String := [
 231  "Dark energy required for Ω = 1 (adds ~70% of critical density)",
 232  "Dark matter required (adds ~25% of critical density)",
 233  "Eternal expansion (no Big Crunch)",
 234  "Geometry is fundamental, not emergent"
 235]
 236
 237/-! ## Falsification Criteria -/
 238
 239/-- The RS explanation would be falsified if:
 240    1. Ω ≠ 1 is definitively measured
 241    2. No J-cost minimum at Ω = 1
 242    3. φ-relations to cosmological parameters fail -/
 243structure FlatnessFalsifier where
 244  omega_not_one : Prop  -- Measured Ω ≠ 1 beyond uncertainty
 245  no_cost_minimum : Prop  -- J-cost doesn't favor flatness