The Minimal Power Spectrum: Higher Order Contributions
The Minimal Power Spectrum: Higher Order Contributions
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最小功率谱：高阶贡献
DOI：
10.1086/173622
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
J. Fry
中科院分区：
文献类型：
--
作者：
J. Fry
一段时间以来，人们普遍认为，对于大尺度上没有初始功率的分布，当 k 接近 0 时，重力会在功率谱中产生大约 k(exp 4) 的最小尾部 P(k)。在最近一次将初始功率限制在 k 的有限范围内的数值实验中，Shandarin 和 Melott (1990) 发现 k 接近 0 尾部，在演化的早期阶段表现为 k(exp 4)，并随时间增长为 a(exp 4)(t)，其中 a(t) 是宇宙膨胀因子，而在后期依赖于尺度，如 k(exp 3) 并随时间增长为 a(exp 2)(t)。我分析计算了比早期工作中包含的更高阶功率谱的几个贡献，并将结果应用于初始功率限制在 k 的有限范围的特定情况。正如预期的那样，在微扰状态 P(k) 中，当 k 接近 0 时，来自线性微扰理论第一次修正的大约 a(exp 4)k(exp 4) 是主导项。数值研究表明，高阶贡献也为 k(exp 4)。然而，仅靠微扰理论无法判断 P 近似 a(exp 2)k(exp 3) 结果是“非微扰”还是数值伪影。
It has been an accepted belief for some time that gravity induces a minimal tail P(k) approximately k(exp 4) in the power spectrum as k approaches 0 for distributions with no initial power on large scales. In a recent numerical experiment with initial power confined to a restricted range in k, Shandarin and Melott (1990) found a k approaches 0 tail that at early stages of evolution behaves as k(exp 4) and grows with time as a(exp 4)(t), where a(t) is the cosmological expansion factor, and at late times depends on scale as k(exp 3) and grows with time as a(exp 2)(t). I compute analytically several contributions to the power spectrum of higher order than those included in earlier work, and I apply the results to the particular case of initial power restricted to a finite range of k. As expected, in the perturbative regime P(k) approximately a(exp 4)k(exp 4) from the first correction to linear perturbation theory is the dominant term as k approaches 0. Numerical investigations show that the higher order contributions go as k(exp 4) also. However, perturbation theory alone cannot tell whether the P approximately a(exp 2)k(exp 3) result is 'nonperturbative' or a numerical artifact.