Numerical investigation of non-Gaussianities in the phase and modulus of
  density Fourier modes
  We numerically investigate non-Gaussianities in the late-time cosmological
density field in Fourier space. We explore various statistics, including the
two-point and three-point probability distribution function (PDF) of phase and
modulus, and two \& three-point correlation function of of phase and modulus.
We detect significant non-Gaussianity for certain configurations. We compare
the simulation results with the theoretical expansion series of
\citet{2007ApJS..170....1M}. We find that the $\mathcal{O}(V^{-1/2})$ order
term alone is sufficiently accurate to describe all the measured
non-Gaussianities in not only the PDFs, but also the correlations. We also
numerically find that the phase-modulus cross-correlation contributes $\sim
50\%$ to the bispectrum, further verifying the accuracy of the
$\mathcal{O}(V^{-1/2})$ order prediction. This work demonstrates that
non-Gaussianity of the cosmic density field is simpler in Fourier space, and
may facilitate the data analysis in the era of precision cosmology.
