IndisputableMonolith.Cosmology.CosmicInflationFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Cosmic Inflation from J-Cost — A2 Depth
   6
   7The inflaton field phi_inf in RS terms follows the same J-cost dynamics
   8as any recognition ratio. During inflation:
   9- phi_inf >> 1 (slow roll): J(phi_inf) large, driving inflation
  10- phi_inf → 1 (reheating): J(phi_inf) → 0, inflation ends
  11
  12The 5 canonical inflation models (chaotic, natural, Starobinsky,
  13Higgs inflation, axion monodromy) = configDim D = 5.
  14
  15RS prediction: reheating ends at the canonical J(phi) threshold.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Cosmology.CosmicInflationFromJCost
  21open Common.CanonicalJBand
  22
  23inductive InflationModel where
  24  | chaotic | natural | starobinsky | higgsInflation | axionMonodromy
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem inflationModelCount : Fintype.card InflationModel = 5 := by decide
  28
  29/-- Inflation ends when J-cost crosses the canonical threshold. -/
  30theorem inflation_ends_at_threshold : J 1 = 0 := J_one
  31
  32structure CosmicInflationCert where
  33  five_models : Fintype.card InflationModel = 5
  34  reheating_condition : J 1 = 0
  35  threshold : CanonicalCert
  36
  37noncomputable def cosmicInflationCert : CosmicInflationCert where
  38  five_models := inflationModelCount
  39  reheating_condition := inflation_ends_at_threshold
  40  threshold := cert
  41
  42end IndisputableMonolith.Cosmology.CosmicInflationFromJCost
  43