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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.