  In the standard paradigm for cosmological structure formation, clustering
develops from initially random-phase (Gaussian) density fluctuations in the
early Universe by a process of gravitational instability. The later, non-linear
stages of this process involve Fourier mode-mode interactions that result in a
complex pattern of non-random phases. We present a novel mapping technique that
reveals mode coupling induced by this form of nonlinear interaction and allows
it to be quantified statistically. The phase mapping technique circumvents the
difficulty of the circular characteristic of phi_k and illustrates the
statistical significance of phase difference at the same time. This generalized
method on phases allows us to detect weak coupling of phases on any Delta k
scales.
