Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis
Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis
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DOI：
10.1103/physrevd.77.024022
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发表时间：
2007-07
影响因子：
5
通讯作者：
T. Harada;H. Maeda;B. Carr
中科院分区：
文献类型：
--
作者：
T. Harada;H. Maeda;B. Carr
在常微分方程组的渐近分析的基础上，我们将爱因斯坦方程的所有球对称自相似解分类，这些解在大距离上是渐近Friedmann的，并且包含状态方程为p=({Gamma}-1){Mu}(0 1)的理想流体。然而，在后一种情况下，存在一个与音速点处的弱不连续有关的附加参数，解仅是渐近的“准Friedmann”，即它们在很大距离上表现出角度亏损。在0<；{Gamma}<；2/3的情况下，不存在音速点，并且存在一个单参数解族，它们在很大距离上是真正渐近的Friedmann解。我们发现了八类渐近行为：大距离的Friedmann或准Friedmann或准静态或常速度，小距离的准Friedmann或正质量奇异或负质量奇异，以及中距离的准Kantowski-Sachs。自相似渐近准静态和准Kantowski-Sachs解在解析上是可推广的，并且具有很大的宇宙学意义。我们还研究了它们的共形图。本分析的结果被用在另一篇附文中，以获得和物理解释数值解。
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=({gamma}-1){mu} with 0 1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically 'quasi-Friedmann', in the sense that they exhibit an angle deficit at large distances. In the 0<{gamma}<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in anmore » accompanying paper to obtain and physically interpret numerical solutions.« less