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arXiv 0903.5296astro-ph.COgr-qchep-phhep-th
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广义相对论中尺度相关增长函数的新参数化

New Parametrization for the Scale Dependent Growth Function in General Relativity

James B. Dent, Sourish Dutta, Leandros Perivolaropoulos

备注：
Revised and extended version. No changes in results. 7 pages, 4 figures. The mathematica files used for the production of the figures may be downloaded from http://leandros.physics.uoi.gr/newpar.zip
发表信息：
Phys.Rev.D80:023514,2009
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摘要：

我们证明了基于广义相对论的暗能量模型中宇宙学扰动扰增长函数的尺度依赖性。这种尺度依赖性在$100h^{-1}Mpc$或更大的宇宙学尺度上更为突出。我们推导出一个新的尺度相关的参数化，推广了众所周知的牛顿近似结果$f_0(a)\equiv \frac{d\ln δ_0}{d\ln a}=\om(a)^γ$（$γ={6/11}$为\lcdm），这是一个很好的近似尺度小于$50h^{-1}Mpc$。我们的广义参数化是$f(a)=\frac{f_0(a)}{1+ξ(a,k)}$的形式，其中$ξ(a,k)=\frac{3 H_{0}^{2} \omm}{a k^2}$。我们表明，这种参数化适合的增长函数的完全广义相对论评价的确切结果，以地平线尺度为\lcdm和动态暗能量。相比之下，尺度无关参数化在超过层位尺度（$k\simeq 0.01 h^{-1}Mpc$）的5%的尺度上不提供良好的拟合。

英文摘要：

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 $f_0(a)\equiv \frac{d\ln δ_0}{d\ln a}=\om(a)^γ$ ($γ={6/11}$ for \lcdm) which is a good approximation on scales less than $50h^{-1}Mpc$. Our generalized parametrization is of the form $f(a)=\frac{f_0(a)}{1+ξ(a,k)}$ where $ξ(a,k)=\frac{3 H_{0}^{2} \omm}{a k^2}$. 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 ($k\simeq 0.01 h^{-1}Mpc$).

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