On Second-Order Perturbation Theories of Gravitational Instability in Friedmann-Lemaître Models
On Second-Order Perturbation Theories of Gravitational Instability in Friedmann-Lemaître Models
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Friedmann-Lemaître 模型中引力不稳定性的二阶微扰理论
DOI：
10.1143/ptp.94.1151
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发表时间：
1995
影响因子：
--
通讯作者：
T. Matsubara
中科院分区：
文献类型：
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作者：
T. Matsubara
欧拉和拉格朗日二阶微扰理论在 $\Omega \neq 1$ 和 $\Lambda \neq 0$ {}Friedmann-Lema\^{\i}tre 模型中以封闭形式明确求解。我明确地用封闭一维积分来写二阶理论。在宇宙学感兴趣的情况下（$\Lambda = 0$ 或 $\Omega + \lambda = 1$），它们简化为初等函数或超几何函数。对于任意$\Omega$和$\Lambda$，我提出了精确的拟合公式，足以满足观测宇宙学的实践。对于感兴趣的通用 $\Omega$ 和 $\Lambda$ 再次确认二阶效应仅弱依赖于这些参数。
The Eulerian and Lagrangian second-order perturbation theories are solved explicitly in closed forms in $\Omega \neq 1$ and $\Lambda \neq 0$ {}Friedmann-Lema\^{\i}tre models. I explicitly write the second-order theories in terms of closed one-dimensional integrals. In cosmologically interested cases ($\Lambda = 0$ or $\Omega + \lambda = 1$), they reduce to elementary functions or hypergeometric functions. For arbitrary $\Omega$ and $\Lambda$, I present accurate fitting formula which are sufficient in practice for the observational cosmology. It is reconfirmed for generic $\Omega$ and $\Lambda$ of interest that second-order effect only weakly depends on these parameters.