New Parametrization for the Scale Dependent Growth Function in General
  Relativity
  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 ($k\simeq 0.01 h^{-1}Mpc$).
