宇宙学物质密度场的Copula是非高斯的
The copula of the cosmological matter density field is non-Gaussian
摘要：
宇宙学物质密度场的非高斯性可以通过局部高斯化变换（及其近似，如对数变换）大大减少。这种行为可以被重新塑造为高斯Copula假设，并已在两点水平上被验证为非常高的准确性。另一方面，在高斯化场的统计上显著的非高斯性已经在模拟中被检测到。我们指出，这种明显的不一致性是由copula函数中非常有限的自由度引起的，这使得它作为高斯化场中剩余非高斯性的诊断而具有误导性。使用Copula密度，我们强调了高斯性的偏离。我们进一步量化其在预测的n点关联函数的影响。我们探索了高斯copula假设的一种补救方法，它解释了上述问题，但并没有完全解决。
英文摘要：
Non-Gaussianity of the cosmological matter density field can be largely reduced by a local Gaussianization transformation (and its approximations such as the logrithmic transformation). Such behavior can be recasted as the Gaussian copula hypothesis, and has been verified to very high accuracy at two-point level. On the other hand, statistically significant non-Gaussianities in the Gaussianized field have been detected in simulations. We point out that, this apparent inconsistency is caused by the very limited degrees of freedom in the copula function, which make it misleading as a diagnosis of residual non-Gaussianity in the Gaussianized field. Using the copula density, we highlight the departure from Gaussianity. We further quantify its impact in the predicted n-point correlation functions. We explore a remedy of the Gaussian copula hypothesis, which alleviates but not completely solves the above problems.
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