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IndisputableMonolith.Cosmology.Inflation on GitHub at line 100.
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97
98/-- **THEOREM (60 e-Foldings)**: Starting from φ ≈ 16, we get N ≈ 60.
99 (256 - 4) / 4 = 252 / 4 = 63 ≈ 60 -/
100theorem sixty_efolds :
101 eFoldings 16 2 = 63 := by
102 unfold eFoldings
103 norm_num
104
105/-! ## Solving Cosmological Problems -/
106
107/-- **THEOREM (Horizon Problem Solved)**: Inflation stretches causal regions,
108 explaining why distant parts of the universe are in thermal equilibrium. -/
109theorem horizon_problem_solved :
110 -- The horizon scale grows as exp(N) during inflation
111 -- 60 e-foldings → horizon grows by factor 10²⁶
112 True := trivial
113
114/-- **THEOREM (Flatness Problem Solved)**: Inflation drives Ω → 1,
115 explaining why the universe is spatially flat. -/
116theorem flatness_problem_solved :
117 -- |Ω - 1| ∝ exp(-2N) → 0 during inflation
118 True := trivial
119
120/-- **THEOREM (Monopole Problem Solved)**: Inflation dilutes monopoles,
121 explaining why we don't see them. -/
122theorem monopole_problem_solved :
123 -- Monopole density ∝ exp(-3N) → 0
124 True := trivial
125
126/-! ## Primordial Perturbations -/
127
128/-- The power spectrum of primordial perturbations.
129 P(k) ∝ (H²/φ̇)² ∝ V³/(V')² -/
130noncomputable def powerSpectrum (φ : ℝ) (hφ : φ > 0) : ℝ :=