Dark matter growth and baryon bias in an accelerating universe

We investigate the exact analytic solutions for the growths of the dark matter and the baryon in sub-horizon scale. The growth of the dark matter $\delta_{\DM}$ is related to that of the halos. Thus, the exact solution for the growth of the dark matter is important to obtain the proper properties of dark matter halos. However, the dark energy model dependence of $\delta_{\DM}$ is confused with the $\delta_{\DM}$ dependence on $\Omega_{m}^{0}$. Thus, the careful investigation is necessary for the $\delta_{\DM}$ dependence on dark energy models. We also obtain the exact solution of the growth of the baryon $\delta_{\B}$ which can be used to obtain the baryon bias factor $b(a)$. This might be able to be observed in intracluster gas or in Lyman-$\alpha$ clouds. However, $b(a)$ is quite model independent. Recently, we obtained the exact analytic solution for the growing mode solution of the matter linear density perturbation $\delta$ on sub-horizon scale for general dark energy model \cite{SK}. This solution is not same as the well known approximate analytic solution \cite{Waga}. The exact analytic solution shows the same evolution behavior of the growth factor obtained numerically. However, the exact solution is simple and useful for the extension to other models including modified gravity theories. Furthermore, it guides to the fact that the growth index parameter depends on both models $\omega_{\de}$ and $\Omega_{m}^{0}$ and thus we need to be careful for applying the fitting formulae to the general models \cite{WS}. The exact analytic solutions for the growth factor will provide the more accurate tools for the weak lensing, the number density of clusters, their mass and etc.