AI 中文总结
该研究计算宇宙密度和速度场方差的首个非线性修正，通过对称化三阶微扰核并识别发散项抵消，发现密度场线性方差修正系数在1.817至1.843的窄范围内。
AI 中文摘要
背景：非线性引力演化影响密度和速度涨落的增长，并在维里化结构形成之前导致预维里化效应。因此，理解和量化对应方差的主要非线性修正是描述偏离线性结构形成的关键。目的：我们计算宇宙密度场和速度场方差的首个非线性修正。方法：我们分析了与密度场和速度散度场的二阶和三阶微扰核相关的单圈贡献。密度场的三阶核F3和速度散度场的三阶核G3的相关形式在k与q交换下明显不对称。然而，方差的计算涉及这些变量的对称二重积分，因此在这种特殊情况下，核可以额外对称化。因此，我们显式地对称化这些核F3和G3，并将它们表示为两个标量变量的函数：两个波矢之间夹角的余弦以及它们幅度的对称函数。这种表示使我们能够识别并分离出在角度积分之前发散的项，并展示它们在二阶和三阶项之间的抵消。结果：来自Pdelta22的单圈功率谱的发散贡献恰好抵消了来自Pdelta13的贡献。F3的角平均无散部分非常接近常数。结论：对于任何形式的线性功率谱，密度场线性方差非线性修正的系数在1.817到1.843的窄范围内。
英文摘要
Non-linear gravitational evolution affects the growth of density and velocity fluctuations, and leads to previrialization effects before virialized structures are formed. Therefore, understanding and quantifying the leading nonlinear corrections to the corresponding variances is crucial for describing the departure from linear structure formation. We calculate the first nonlinear correction to the variance of the cosmic density and velocity fields. We analyze the 1-loop contributions associated with the second and third order perturbative kernels of both the density and velocity-divergence fields. The relevant forms of the third-order kernels $F_3(\vec{k},\vec{q},-\vec{q})$ for density, and $G_3(\vec{k},\vec{q},-\vec{q})$ for velocity divergence, are clearly non-symmetric under exchange of $\vec{k}$ with $\vec{q}$. However, the calculation of the variance involves a symmetric double integral of these variables, so in this particular case the kernels can be additionally symmetrized. We therefore explicitly symmetrize these kernels $F_3$ and $G_3$, and express them as functions of the two scalar variables: the cosine of the angle between the two wavevectors and a symmetric function of their magnitudes. This representation enables us to identify and isolate the terms which are divergent before performing the angular integration, and to show their cancellation between the second- and third-order terms. The divergent contribution from $P_{δ22}\,$ to the one-loop power spectrum cancels exactly that arising from $P_{δ13}$ . Angularly averaged divergence-free part of $F_3$ turns out to be remarkably close to a constant. We found that the corresponding coefficient of the leading-order correction is confined to a remarkably narrow interval of 4007/2205 to 4063/2205 $(\simeq 1.817 \leq C \leq 1.843)$, for any form of the linear power spectrum.
Comments4 pages, 1 figure, 2 tables, to be submitted to Astronomy & Astrophysics
