arXiv 1505.033232015-05gr-qcastro-ph.CO

$f(R)$理论中的宇宙学扰动和准静态假设

Cosmological Perturbations and Quasi-Static Assumption in $f(R)$ Theories

Mu-Chen Chiu, Andy Taylor, Chenggang Shu, Hong Tu

DOI：: 10.1103/PhysRevD.92.103514

摘要：

$f(R)$引力是修正引力理论中解释宇宙加速膨胀的最简单的理论之一。虽然通常假设宇宙微扰的准牛顿方法（准静态近似和亚哈勃极限的结合）足以描述$f(R)$模型中大尺度结构的演化，但一些研究表明，这种方法并不适用于所有的$f(R)$模型。在这里，我们表明，在物质占主导地位的时代，压力和剪切方程，这可以被改写成四个一阶方程，以解决宇宙学扰动准确，是足以解决牛顿势，$Ψ$，和曲率的潜力，$Φ$。基于这两个方程，我们能够阐明精确的线性扰动如何适应不同的极限。我们发现康普顿长度控制了$f(R)$引力的准静态行为。此外，无论准静态近似的有效性，一个强版本的子哈勃极限本身就足以减少任何可行的$f(R)$重力的精确线性扰动到二阶。我们的研究结果不同意一些以前的研究，我们发现我们的精确和准牛顿的解决方案之间的差异很小，甚至高达$k=10 c^{-1} \mathcal{H}_0$。

英文摘要：

$f(R)$ gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasi-static approximation and sub-Hubble limit) for cosmic perturbations is good enough to describe the evolution of large scale structure in $f(R)$ models, some studies have suggested that this method is not valid for all $f(R)$ models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, $Ψ$, and the curvature potential, $Φ$. Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that the Compton length controls the quasi-static behaviours in $f(R)$ gravity. In addition, regardless the validity of quasi-static approximation, a strong version of the sub-Hubble limit alone is sufficient to reduce the exact linear perturbations in any viable $f(R)$ gravity to second order. Our findings disagree with some previous studies where we find little difference between our exact and quasi-Newtonian solutions even up to $k=10 c^{-1} \mathcal{H}_0$.

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