  We demonstrate the scale dependence of the growth function of cosmological
perturbations in dark energy models based on General Relativity. This scale
dependence is more prominent on cosmological scales of $100h^{-1}Mpc$ or
larger. We derive a new scale dependent parametrization which generalizes the
well known Newtonian approximation result $f_0(a)\equiv \frac{d\ln
\delta_0}{d\ln a}=\om(a)^\gamma$ ($\gamma ={6/11}$ for \lcdm) which is a good
approximation on scales less than $50h^{-1}Mpc$. Our generalized
parametrization is of the form $f(a)=\frac{f_0(a)}{1+\xi(a,k)}$ where
$\xi(a,k)=\frac{3 H_{0}^{2} \omm}{a k^2}$. We demonstrate that this
parametrization fits the exact result of a full general relativistic evaluation
of the growth function up to horizon scales for both \lcdm and dynamical dark
energy. In contrast, the scale independent parametrization does not provide a
good fit on scales beyond 5% of the horizon scale ($k\simeq 0.01 h^{-1}Mpc$).
