code: def _minimize_c(c, z=0, a_tilde=1, b_tilde=-1,
                  Ascaling=900, omega_M_0=0.25, omega_lambda_0=0.75):
      
  
      # Fn 1 (LHS of Eqn 18)
  
      Y1 = np.log(2) - 0.5
      Yc = np.log(1+c) - c/(1+c)
      f1 = Y1/Yc
  
      # Fn 2 (RHS of Eqn 18)
  
      # Eqn 14 - Define the mean inner density
      rho_2 = 200 * c**3 * Y1 / Yc
  
      # Eqn 17 rearranged to solve for Formation Redshift
      # essentially when universe had rho_2 density
      zf = (((1 + z)**3 + omega_lambda_0/omega_M_0) *
            (rho_2/Ascaling) - omega_lambda_0/omega_M_0)**(1/3) - 1
  
      # RHS of Eqn 19
      f2 = ((1 + zf - z)**a_tilde) * np.exp((zf - z) * b_tilde)
  
      # LHS - RHS should be zero for the correct concentration
      return(f1-f2)
docs: Trial function to solve 2 eqns (17 and 18) from Correa et al. (2015c)
          for 1 unknown, i.e. concentration, returned by a minimisation call