We present a calculation of the first-order non-linear interactions between density perturbations in an expanding, Newtonian cosmology. We show that these terms are always negligible if the power falls off less steeply than k4 at small wavenumber, and if |δρ/ρ| is less than one at all scales larger than the scale in question.
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Ethan T. Vishniac (1983) studied this question.