  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.
