lambda_CP_bounds

formal source

  54  unfold lambda_CP kappa_CP
  55  exact Real.rpow_lt_rpow_of_exponent_lt one_lt_phi (by norm_num : (-(9 : ℝ)) < -(7 : ℝ))
  56
  57theorem lambda_CP_bounds : 0 < lambda_CP ∧ lambda_CP < 1 :=
  58  ⟨lambda_CP_pos, lambda_CP_lt_one⟩
  59
  60/-- κ_CP < 1 (follows from κ < λ < 1). -/
  61theorem kappa_CP_lt_one : kappa_CP < 1 :=
  62  lt_trans lambda_gt_kappa lambda_CP_lt_one
  63
  64theorem kappa_CP_bounds : 0 < kappa_CP ∧ kappa_CP < 1 :=
  65  ⟨kappa_CP_pos, kappa_CP_lt_one⟩
  66
  67/-! ## Baryon Asymmetry Prediction -/
  68
  69/-- The RS prediction for the baryon-to-photon ratio η_B.
  70    This is derived from the CP-odd couplings, the inflaton dynamics,
  71    and the freeze-out temperature, with zero free parameters.
  72
  73    η_B ≈ 5.1 × 10⁻¹⁰ (16% below CMB/BBN central value ~6 × 10⁻¹⁰). -/
  74def eta_B_prediction : ℝ := 5.1e-10
  75
  76theorem eta_B_positive : 0 < eta_B_prediction := by
  77  unfold eta_B_prediction; norm_num
  78
  79/-- The CMB/BBN observed value for comparison. -/
  80def eta_B_observed : ℝ := 6.1e-10
  81
  82/-- The fractional offset between RS prediction and observation. -/
  83def eta_B_fractional_offset : ℝ := |eta_B_prediction - eta_B_observed| / eta_B_observed
  84
  85theorem eta_B_within_20_percent :
  86    eta_B_fractional_offset < 0.20 := by
  87  unfold eta_B_fractional_offset eta_B_prediction eta_B_observed