  35theorem efoldCount_eq : efoldCount = 44 := rfl
  36
  37/-- Slow-roll parameter ε = 1/(2φ⁵). -/
  38noncomputable def slowRollEpsilon : ℝ := 1 / (2 * phi ^ 5)
  39
  40/-- Slow-roll parameter η = 1/φ⁵. -/
  41noncomputable def slowRollEta : ℝ := 1 / phi ^ 5
  42
  43/-- φ⁵ = 5φ + 3 (Fibonacci identity). -/
  44theorem phi5_eq : phi ^ 5 = 5 * phi + 3 := by
  45  have h2 := phi_sq_eq
  46  have h3 : phi ^ 3 = 2 * phi + 1 := by nlinarith
  47  have h4 : phi ^ 4 = 3 * phi + 2 := by nlinarith
  48  nlinarith
  49
  50theorem slowRollEpsilon_pos : 0 < slowRollEpsilon := by
  51  unfold slowRollEpsilon
  52  apply div_pos one_pos
  53  exact mul_pos (by norm_num) (pow_pos phi_pos 5)
  54
  55theorem slowRollEta_pos : 0 < slowRollEta := by
  56  unfold slowRollEta
  57  exact div_pos one_pos (pow_pos phi_pos 5)
  58
  59/-- n_s - 1 = -2/45 gives n_s ∈ (0.955, 0.957). -/
  60theorem spectralIndex_band :
  61    ((0.955 : ℝ) < 1 - 2/45) ∧ (1 - 2/45 < (0.957 : ℝ)) := by
  62  refine ⟨?_, ?_⟩ <;> norm_num
  63
  64structure InflatonCert where
  65  five_regimes : Fintype.card InflatonRegime = 5
  66  efolds : efoldCount = 44
  67  phi5_fibonacci : phi ^ 5 = 5 * phi + 3
  68  epsilon_pos : 0 < slowRollEpsilon

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.