${{\mit \Omega}}_{\rm K0} = {{\mit \Omega}}_{\rm M0} + {{\mit \Omega}}_{\rm Q0} - 1$ is the curvature parameter.

The linear growth factor $D(z)$ is a growing solution of the ordinary differential equation, $$\ddot{D} + 2 H(z) \dot{D} - \frac{3}{2} {H_0}^2 {{\mit \Omega}}_{\rm M0} (1 +
   z)^3 D = 0,
\label{eq3-6}$$ where the dot represents the differentiation with respect to the proper time $t$, and the proper time $t$ is related to the RW redshift $z$ by $$t = \int_z^\infty \frac{dz'}{(1 + z')H(z')}.
\label{eq3-7}$$ It is useful to transform the equation (\[eq3-6\]) to the following set of equations [@mat03], $$\begin{aligned}
&&
  \frac{d\ln D}{d\ln a} = f,
\label{eq3-8a}\\
&&
  \frac{df}{d\ln a} = -f^2 - \left(1 - \frac{{{\mit \Omega}}_{\rm M}}{2} -
  \frac{1 + 3 w}{2} {{\mit \Omega}}_{\rm Q} \right) f +
  \frac{3}{2} {{\mit \Omega}}_{\rm M}, 
\label{eq3-8b}\end{aligned}$$ where $a = (1 + z)^{-1}$ is the scale factor of the universe, and $$\begin{aligned}
&&
  {{\mit \Omega}}_{\rm M}(z) = \frac{{H_0}^2}{H^2(z)} (1+z)^3 {{\mit \Omega}}_{\rm M0}
\label{eq3-9a}\\
&&
  {{\mit \Omega}}_{\rm Q}(z) =
  \frac{{H_0}^2}{H^2(z)}
  \exp\left(3\int_0^z \frac{1+w}{1+z} dz\right)
  {{\mit \Omega}}_{\rm Q0}
\label{eq3-9b}\end{aligned}$$ are the time-dependent density parameters of matter and dark energy, respectively. Determining both the growth factor, $D(z)$, and the logarithmic derivative of the growth factor, $f(z)$, is neccesary in 