ReionizationEpoch

formal source

  16namespace IndisputableMonolith.Cosmology.ReionizationHistoryFromRS
  17open Constants
  18
  19inductive ReionizationEpoch where
  20  | darkAges
  21  | firstStars
  22  | galaxyFormation
  23  | bulkReionization
  24  | saturation
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem reionizationEpoch_count :
  28    Fintype.card ReionizationEpoch = 5 := by decide
  29
  30noncomputable def boundaryRedshift (k : ℕ) : ℝ := phi ^ k
  31
  32theorem redshift_ratio (k : ℕ) :
  33    boundaryRedshift (k + 1) / boundaryRedshift k = phi := by
  34  unfold boundaryRedshift
  35  have hpos : (0 : ℝ) < phi ^ k := pow_pos phi_pos k
  36  rw [div_eq_iff hpos.ne', pow_succ]
  37  ring
  38
  39theorem redshift_pos (k : ℕ) : 0 < boundaryRedshift k :=
  40  pow_pos phi_pos k
  41
  42structure ReionizationCert where
  43  five_epochs : Fintype.card ReionizationEpoch = 5
  44  phi_ratio : ∀ k, boundaryRedshift (k + 1) / boundaryRedshift k = phi
  45  boundary_always_pos : ∀ k, 0 < boundaryRedshift k
  46
  47noncomputable def reionizationCert : ReionizationCert where
  48  five_epochs := reionizationEpoch_count
  49  phi_ratio := redshift_ratio