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.
