An application of Wiener Hermite expansion to the nonlinear evolution of dark matter
An application of Wiener Hermite expansion to the nonlinear evolution of dark matter
复制标题
维纳埃尔米特展开式在暗物质非线性演化中的应用
DOI：
10.1088/0004-637x/760/2/114
复制
发表时间：
2012
影响因子：
4.9
通讯作者：
杉山尚徳・二間瀬敏史
中科院分区：
文献类型：
--
作者：
Shimizu;T.;杉山尚徳・二間瀬敏史
我们将维纳埃尔米特（WH）展开应用于大尺度结构的非线性演化，并获得了展开全阶的物质功率谱的近似表达式。该方法允许我们根据随机函数空间中的标准正交基来展开任何随机函数，使得展开的一阶表示高斯分布，其他阶表示与高斯分布的偏差。证明了WH展开在数学上等价于重整化微扰理论(RPT)中的Γ展开方法。虽然 RPT 中暗物质的质量密度和速度涨落的高 k 极限指数行为已被证明，但我们使用标准微扰理论 (SPT) 的结果在 WH 展开的背景下再次证明了该行为。我们提出了一种新的物质功率谱近似表达式，该表达式插入了与 SPT 中 1 环级别相对应的低 k 表达式和通过取 WH 展开的高 k 极限获得的高 k 表达式。通过与 SPT 的 2 环解进行比较，具体验证了我们处方的有效性。所提出的功率谱与 N 体模拟的结果一致，在重子声振荡尺度范围内精度优于 1% 或 2%，其中波数在 z= 0.5-3.0 时约为 k= 0.2-0.4 h Mpc− 1。该精度与闭包理论中的精度相当或略低，与N体结果的分数差在1%以内。我们的方法的一个优点是计算时间非常短，因为我们的解决方案只涉及单积分和双积分。
We apply the Wiener Hermite (WH) expansion to the nonlinear evolution of the large-scale structure and obtain an approximate expression for the matter power spectrum in the full order of the expansion. This method allows us to expand any random function in terms of an orthonormal basis in the space of random functions in such a way that the first order of the expansion expresses the Gaussian distribution, and others are the deviations from Gaussianity. It is proved that the WH expansion is mathematically equivalent to the Γ-expansion approach in the renormalized perturbation theory (RPT). While exponential behavior in the high-k limit has been proved for the mass density and velocity fluctuations of dark matter in the RPT, we prove the behavior again in the context of the WH expansion using the result of the standard perturbation theory (SPT). We propose a new approximate expression for the matter power spectrum which interpolates the low-k expression corresponding to the 1-loop level in SPT and the high-k expression obtained by taking a high-k limit of the WH expansion. The validity of our prescription is specifically verified by comparing with the 2-loop solutions of the SPT. The proposed power spectrum agrees with the result of the N-body simulation with accuracy better than 1% or 2% in a range of baryon acoustic oscillation scales, where the wave number is about k= 0.2–0.4 h Mpc− 1 at z= 0.5–3.0. This accuracy is comparable to or slightly less than the ones in the closure theory, the fractional difference of which from the N-body result is within 1%. One merit of our method is that the computational time is very short because only single and double integrals are involved in our solution.