大尺度结构中摄动理论的分歧
Divergence of Perturbation Theory in Large Scale Structures
摘要：
我们对大尺度结构的微扰理论的有效性和一些非微扰修正的性质的制度的分析理解取得了进展。我们限制自己的一维引力坍缩，壳交叉前的精确解是已知的。我们回顾了最近由McQuinn和White证明的功率谱微扰理论的收敛性，并将其扩展到非高斯初始条件和双谱。与此相反，我们证明了微扰理论发散的实空间两点关联函数和概率密度函数（PDF）的细胞中平均的密度和所有的累积量来自it.We属性这些分歧的统计平均内在的宇宙学观测值，即使在非常大的和“微扰”的规模，给非零的重量，所有极端的波动。最后讨论了实空间和傅立叶空间中非微扰效应的一般性质。
英文摘要：
We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White, and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.
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