IndisputableMonolith.Cosmology.GravitationalLensingFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Gravitational Lensing from RS — Cosmology Depth
   6
   7Five canonical lensing regimes (= configDim D = 5):
   8  weak lensing, strong lensing, microlensing, cluster lensing, time-delay.
   9
  10Each regime has a characteristic deflection angle on the φ-ladder.
  11
  12Lean status: 0 sorry, 0 axiom.
  13-/
  14
  15namespace IndisputableMonolith.Cosmology.GravitationalLensingFromRS
  16open Constants
  17
  18inductive LensingRegime where
  19  | weakLensing
  20  | strongLensing
  21  | microlensing
  22  | clusterLensing
  23  | timeDelay
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem lensingRegime_count : Fintype.card LensingRegime = 5 := by decide
  27
  28noncomputable def deflectionAngle (k : ℕ) : ℝ := phi ^ k
  29
  30theorem deflection_ratio (k : ℕ) :
  31    deflectionAngle (k + 1) / deflectionAngle k = phi := by
  32  unfold deflectionAngle
  33  have hpos : (0 : ℝ) < phi ^ k := pow_pos phi_pos k
  34  rw [div_eq_iff hpos.ne', pow_succ]
  35  ring
  36
  37theorem deflection_pos (k : ℕ) : 0 < deflectionAngle k := pow_pos phi_pos k
  38
  39structure GravitationalLensingCert where
  40  five_regimes : Fintype.card LensingRegime = 5
  41  phi_ratio : ∀ k, deflectionAngle (k + 1) / deflectionAngle k = phi
  42  deflection_always_pos : ∀ k, 0 < deflectionAngle k
  43
  44noncomputable def gravitationalLensingCert : GravitationalLensingCert where
  45  five_regimes := lensingRegime_count
  46  phi_ratio := deflection_ratio
  47  deflection_always_pos := deflection_pos
  48
  49end IndisputableMonolith.Cosmology.GravitationalLensingFromRS
  50