If the cosmic density field in the nonlinear regime is described by the halo model, the nonlinear evolution of the cosmic gravitational clustering in the phase space, i.e. the k-x (scale-position) space, basically is spatially local. That is, if viewing the mass field with modes in the phase space, the nonlinear evolution will cause strong coupling among modes with different scale k, but at the same physical x area, while the modes at different position x remain uncorrelated, or very weak correlated if the initial perturbations are Gaussian. This locality is due to the self-similar and hierarchical features of the cosmic gravitational clustering.
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