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There have been the approximate analytic solution \cite{Silveria} and severalapproximate analytic forms \cite{0508156,Carroll,0303112} of the growth factor$D_{g}$ for the general dark energy models with the constant values of itsequation of state $\omde$ after Heath found the exact integral form of thesolution of $D_{g}$ for the Universe including the cosmological constant or thecurvature term. Recently, we obtained the exact analytic solutions of thegrowth factor for both $\omde = -1$ or $-\fr{1}{3}$ \cite{SK1} and the generaldark energy models with the constant equation of state $\omde$ \cite{SK3}independently. We compare the exact analytic solution of $D_{g}$ with the otherwell known approximate solutions. We also prove that the analytic solutions for$\omde = -1$ or $-\fr{1}{3}$ in Ref. \cite{SK1} are the specific solutions ofthe exact solutions of the growth factor for general $\omde$ models in Ref.\cite{SK3} even though they look quite different. We scrutinize the issue ofusing the well known parameterizations of the growth index and its parametergiven in Ref. \cite{WS} to obtain the growth factor for general dark energymodels. We also investigate the possible extensions of the exact solution of$D_{g}$ to the time-varying $\omde$ for the comparison with observations.

Properties of the exact analytic solution of the growth factor and its applications