The Copula of the Cosmological Matter Density Field is Non-Gaussian

Non-Gaussianity of the cosmological matter density field can be largely reduced by a local Gaussianization transformation (and its approximations, such as the logarithmic transformation). Such behavior can be recast as the Gaussian copula hypothesis (GCH), and has been verified to very high accuracy at a 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 and at the two-point level, we highlight the departure from Gaussianity. We further quantify its impact in the predictednth (n >= 2) order correlation functions. We explore a remedy of the GCH, which alleviates but does not completely solve the above problems.