strainAtScale

formal source

  71
  72    For k ≪ k_8: Q ≈ 0 (large scales, no suppression)
  73    For k ≫ k_8: Q ≈ J_max (small scales, maximum suppression) -/
  74noncomputable def strainAtScale (k k8 : ℝ) : ℝ :=
  75  if k ≤ k8 then 0 else Jcost (k / k8)
  76
  77/-- The maximum strain from a single 8-tick cycle.
  78
  79    Q_max = J(φ) since the maximum stable ratio in a cycle is φ. -/
  80noncomputable def Q_max : ℝ := Jcost phi
  81
  82/-! ## Suppression Factor Derivation -/
  83
  84/-- The growth suppression factor from recognition strain.
  85
  86    f_sup = 1 - Q/Q_max
  87
  88    where Q is the accumulated strain from structure formation. -/
  89noncomputable def suppressionFactor (Q : ℝ) : ℝ := 1 - Q / Q_max
  90
  91/-- The predicted σ₈ after RS suppression. -/
  92noncomputable def sigma8_predicted (Q : ℝ) : ℝ :=
  93  sigma8_cmb * suppressionFactor Q
  94
  95/-! ## The Calibrated Strain -/
  96
  97/-- The maximum theoretical strain (normalized to 1 for convenience). -/
  98noncomputable def Q_max_normalized : ℝ := 1
  99
 100/-- The suppression factor using normalized strain.
 101    f_sup = 1 - Q/1 = 1 - Q -/
 102noncomputable def suppressionFactorNorm (Q : ℝ) : ℝ := 1 - Q
 103
 104/-- The effective recognition strain for σ₈ scales (k ≈ 0.2 h/Mpc).