增长因子精确解析解的性质及其应用
Properties of the exact analytic solution of the growth factor and its applications
摘要：
Heath发现了包含宇宙学常数或曲率项的$D_{g}$解的精确积分形式后，对于状态方程为常数的一般暗能量模型，已有了$D_{g}$的近似解析解\cite{Silveria}和几种近似解析形式\cite{0508156,Carroll,0303112}。最近，我们分别得到了$\omde = -1$和$-\fr{1}{3}$ \cite{SK1}的生长因子的精确解析解，以及具有常值状态方程$\omde$ \cite{SK3}的一般暗能量模型的生长因子的精确解析解.我们比较了$D_{g}$的精确解析解与其他已知的近似解。我们还证明了文献\cite{SK1}中的$\omde = -1$或$-\fr{1}{3}$的解析解是文献\cite{SK3}中一般$\omde$模型的生长因子的精确解的特解，尽管它们看起来很不一样.我们仔细研究的问题，使用众所周知的参数化的增长指数和它的参数，在参考文献\cite{WS}，以获得一般的暗能量模型的增长因子。我们还研究了$D_{g}$的精确解的可能的扩展到随时间变化的$\omde$与观察比较。
英文摘要：
There have been the approximate analytic solution \cite{Silveria} and several approximate analytic forms \cite{0508156,Carroll,0303112} of the growth factor $D_{g}$ for the general dark energy models with the constant values of its equation of state $\omde$ after Heath found the exact integral form of the solution of $D_{g}$ for the Universe including the cosmological constant or the curvature term. Recently, we obtained the exact analytic solutions of the growth factor for both $\omde = -1$ or $-\fr{1}{3}$ \cite{SK1} and the general dark energy models with the constant equation of state $\omde$ \cite{SK3} independently. We compare the exact analytic solution of $D_{g}$ with the other well 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 of the exact solutions of the growth factor for general $\omde$ models in Ref. \cite{SK3} even though they look quite different. We scrutinize the issue of using the well known parameterizations of the growth index and its parameter given in Ref. \cite{WS} to obtain the growth factor for general dark energy models. We also investigate the possible extensions of the exact solution of $D_{g}$ to the time-varying $\omde$ for the comparison with observations.
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