包含色散与高阶累积量的微扰理论：非线性区域
Perturbation theory with dispersion and higher cumulants: non-linear regime
AI总结：
提出包含色散与高阶累积量的Vlasov微扰理论非线性解，通过UV模式屏蔽机制克服SPT发散，在单圈和双圈阶与N-body结果良好匹配，证明暗物质微扰技术可系统性改进。
摘要：
我们提出了 Vlasov Perturbation Theory (VPT) 的非线性解，用于描述由轨道交叉引起的具有色散和高阶累积量的无碰撞暗物质的引力聚集。我们表明，VPT 可以转化为一种在形式上类似于 Standard Perturbation Theory (SPT) 的形式，但包含了额外的微扰变量、非线性相互作用以及更复杂的传播。VPT 非线性核具有一个关键的解耦性质：在固定总动量的情况下，当任何单个动量越过色散尺度进入非线性区域时，核会受到强烈的抑制。这种 UV 模式的屏蔽效应使我们能够计算功率谱的非线性修正，即使是对于 SPT 发散的具有极蓝幂律输入谱的宇宙学模型也是如此。我们将密度和速度散度功率谱以及单圈阶的 bispectrum 的预测，与具有谱指数 $-1\leq n_s\leq +2$ 的标度宇宙中的 N-body 结果进行了比较。我们发现所有情况在达到非线性尺度之前均表现出良好的一致性，且其适用范围随谱指数 $n_s$ 的增加而扩大。我们讨论了涡度的产生以及速度色散的矢量和张量模式，表明在包含色散时忽略涡度将导致动量守恒的破坏。我们在包含涡度时验证了动量守恒，并计算了双圈阶的涡度功率谱，这对于恢复具有斜率 $n_w=2$ 的正确大尺度极限是必要的。与我们的 N-body 测量结果进行比较，证实了大尺度上从 $k^4$ 到 $k^2$ 标度的跨越。我们的结果提供了原理性证明，即基于已知的底层无碰撞动力学，暗物质聚集的微扰技术可以得到系统性改进。
英文摘要：
We present non-linear solutions of Vlasov Perturbation Theory (VPT), describing gravitational clustering of collisionless dark matter with dispersion and higher cumulants induced by orbit crossing. We show that VPT can be cast into a form that is formally analogous to standard perturbation theory (SPT), but including additional perturbation variables, non-linear interactions, and a more complex propagation. VPT non-linear kernels have a crucial decoupling property: for fixed total momentum, the kernels becomes strongly suppressed when any of the individual momenta cross the dispersion scale into the non-linear regime. This screening of UV modes allows us to compute non-linear corrections to power spectra even for cosmologies with very blue power-law input spectra, for which SPT diverges. We compare predictions for the density and velocity divergence power spectra as well as the bispectrum at one-loop order to N-body results in a scaling universe with spectral indices $-1\leq n_s\leq +2$. We find a good agreement up to the non-linear scale for all cases, with a reach that increases with the spectral index $n_s$. We discuss the generation of vorticity as well as vector and tensor modes of the velocity dispersion, showing that neglecting vorticity when including dispersion would lead to a violation of momentum conservation. We verify momentum conservation when including vorticity, and compute the vorticity power spectrum at two-loop order, necessary to recover the correct large-scale limit with slope $n_w=2$. Comparing to our N-body measurements confirms the cross-over from $k^4$ to $k^2$ scaling on large scales. Our results provide a proof-of-principle that perturbative techniques for dark matter clustering can be systematically improved based on the known underlying collisionless dynamics.
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