非线性物质N点函数的角平均压缩极限
The angle-averaged squeezed limit of nonlinear matter N-point functions
摘要：
我们表明，在一定的角度平均压缩极限，$N$点函数的物质是相关的响应的物质功率谱的长波长密度扰动，$P^{-1}d^nP(k|δ_L)/dδ_L^n|_{δ_L=0}$，与$n=N-2$。通过使用\emph{separate universe}方法在平坦的Friedmann-Robertson-Lemaintre-Walker（FRLW）宇宙上叠加均匀的超密度进行N体模拟，我们获得了直到$n=3$的非线性物质功率谱响应的测量，这相当于测量了在这个压缩极限下完全非线性物质$3-$到$5-$的点函数.这些测量的百分之几到百分之几的准确度是前所未有的。然后，我们测试的假设，在一个给定的时间的非线性$N$ -点函数的线性功率谱的函数在那个时候，这是预测的标准扰动理论（SPT）及其变种，是基于理想的无压流体方程。具体来说，我们比较了从单独的宇宙模拟和模拟与重新缩放的初始（线性）功率谱振幅计算的响应。我们发现$5-$在$k\simeq 0.2 - 0.5 \,h\,{\rm Mpc}^{-1}$的$3-$点函数在$z=0$的差异为10%。该差异发生在$z=2$的较高波数处。因此，SPT及其变体，执行到任意高阶，保证无法描述该尺度附近的物质$N$ -点函数（$N>2$）。
英文摘要：
We show that in a certain, angle-averaged squeezed limit, the $N$-point function of matter is related to the response of the matter power spectrum to a long-wavelength density perturbation, $P^{-1}d^nP(k|δ_L)/dδ_L^n|_{δ_L=0}$, with $n=N-2$. By performing N-body simulations with a homogeneous overdensity superimposed on a flat Friedmann-Robertson-Lemaître-Walker (FRLW) universe using the \emph{separate universe} approach, we obtain measurements of the nonlinear matter power spectrum response up to $n=3$, which is equivalent to measuring the fully nonlinear matter $3-$ to $5-$point function in this squeezed limit. The sub-percent to few percent accuracy of those measurements is unprecedented. We then test the hypothesis that nonlinear $N$-point functions at a given time are a function of the linear power spectrum at that time, which is predicted by standard perturbation theory (SPT) and its variants that are based on the ideal pressureless fluid equations. Specifically, we compare the responses computed from the separate universe simulations and simulations with a rescaled initial (linear) power spectrum amplitude. We find discrepancies of 10\% at $k\simeq 0.2 - 0.5 \,h\,{\rm Mpc}^{-1}$ for $5-$ to $3-$point functions at $z=0$. The discrepancy occurs at higher wavenumbers at $z=2$. Thus, SPT and its variants, carried out to arbitrarily high order, are guaranteed to fail to describe matter $N$-point functions ($N>2$) around that scale.
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