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arXiv 1706.01360gr-qc
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高阶引力理论中的宇宙学渐近性

Cosmological Asymptotics in Higher-Order Gravity Theories

Georgios Kolionis

摘要:

我们研究了在全有效四维高导数引力理论中真空中各向同性和均匀解以及充满辐射的宇宙模型的早期行为。我们使用渐近的方法来分析所有可能的方法,以初始奇异的宇宙。为了做到这一点,我们构造自治动力系统,描述这些模型的演变,并分解相关的向量场。我们证明,在早期,所有的单位真空,以及一般的弯曲的全球吸引的“通用”平方根标度解。另一方面,开放真空在未来和过去的方向上都显示出一种主导的渐近方法,可以从较小维度的初始数据集中获得无视界的米尔恩态。封闭的宇宙表现出更复杂的对数奇点。我们的渐近稳定性的结果表明,可能的关系,循环和ekpyrotic宇宙在通过奇点。在同一类充满辐射的宇宙的情况下,我们证明了所得到的渐近方案的本质唯一性和稳定性,在所有情况下,除了可能是共形不变的巴赫-外尔引力,再一次由$t^{1/2}$主导。在所有情况下,我们构建了一个正式的系列表示有效的初始奇异点附近的这些模型的一般解决方案,并证明曲率以及辐射起着次主导作用的主导形式。本文还讨论了这些结果对理论的一般初始状态的影响。

英文摘要:

We study the early-time behavior of isotropic and homogeneous solutions in vacuum as well as radiation-filled cosmological models in the full, effective, four dimensional gravity theory with higher derivatives. We use asymptotic methods to analyze all possible ways of approach to the initial singularity of such universes. In order to do so, we construct autonomous dynamical systems that describe the evolution of these models, and decompose the associated vector fields. We prove that, at early times, all flat vacua as well as general curved ones are globally attracted by the "universal" square root scaling solution. Open vacua, on the other hand show in both, future and past directions a dominant asymptotic approach to horizon-free, Milne states that emerge from initial data sets of smaller dimension. Closed universes exhibit more complex logarithmic singularities. Our results on asymptotic stability show a possible relation to cyclic and ekpyrotic cosmologies at the passage through the singularity. In the case of radiation-filled universes of the same class we show the essential uniqueness and stability of the resulting asymptotic scheme, once more dominated by $t^{1/2}$, in all cases except perhaps that of the conformally invariant Bach-Weyl gravity. In all cases, we construct a formal series representation valid near the initial singularity of the general solution of these models and prove that curvature as well as radiation play a subdominant role in the dominating form. A discussion is also made on the implications of these results for the generic initial state of the theory.

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。

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