arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0801.4090gr-qcastro-phhep-th
收藏

高阶引力场中各向同性宇宙学奇点的稳定性

The Stability of an Isotropic Cosmological Singularity in Higher-Order Gravity

Jonathan Middleton, John D. Barrow

备注：
25 pages
发表信息：
Phys.Rev.D77:103523,2008
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们研究了引力理论中各向同性真空Friedmann宇宙的稳定性，在接近初始宇宙学奇点时，高阶曲率项的形式为$(R_{ab}R^{ab})^{n}$，加入到广义相对论的Einstein-Hilbert Lagrangian中。前面，我们已经表明，当$% n=1$，一个特殊的各向同性真空解决方案存在的行为像辐射主导的弗里德曼宇宙，是稳定的各向异性和小的非均匀扰动的标量，矢量和张量类型。这与广义相对论中的情形完全不同，在广义相对论中，各向同性的初始宇宙学奇点在真空和广泛的非真空条件下是不稳定的。我们表明，当$n\neq 1$，虽然一个特殊的各向同性真空解发现的克利夫顿和巴罗总是存在的，它不再是稳定的初始奇点时，接近。我们发现的张量，矢量和标量扰动的影响下，一般$n$的两个解决方案分支的特殊稳定性条件。在接近初始奇点时，具有尺度因子$a(t)=t^{P_{-}/3}$的各向同性真空解对$0.5<n< 1.1309$和$0.861425 < n \leq 1$分别是张量扰动和矢量扰动稳定的，而对$t \to 0$则是不稳定的.具有比例因子$a(t)=t^{P_{+}/3}$的解与$n>1$的初始奇异性的情况无关，并且对于每种类型的扰动，对于所有$n$，作为$t \to 0$不稳定。

英文摘要：

We study the stability of the isotropic vacuum Friedmann universe in gravity theories with higher-order curvature terms of the form $(R_{ab}R^{ab})^{n}$ added to the Einstein-Hilbert Lagrangian of general relativity on approach to an initial cosmological singularity. Earlier, we had shown that, when $% n=1$, a special isotropic vacuum solution exists which behaves like the radiation-dominated Friedmann universe and is stable to anisotropic and small inhomogeneous perturbations of scalar, vector and tensor type. This is completely different to the situation that holds in general relativity, where an isotropic initial cosmological singularity is unstable in vacuum and under a wide range of non-vacuum conditions. We show that when $n\neq 1$, although a special isotropic vacuum solution found by Clifton and Barrow always exists, it is no longer stable when the initial singularity is approached. We find the particular stability conditions under the influence of tensor, vector, and scalar perturbations for general $n$ for both solution branches. On approach to the initial singularity, the isotropic vacuum solution with scale factor $a(t)=t^{P_{-}/3}$ is found to be stable to tensor perturbations for $0.5<n< 1.1309$ and stable to vector perturbations for $0.861425 < n \leq 1$, but is unstable as $t \to 0$ otherwise. The solution with scale factor $a(t)=t^{P_{+}/3}$ is not relevant to the case of an initial singularity for $n>1$ and is unstable as $t \to 0$ for all $n$ for each type of perturbation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑