Large-scale structures, observed today, are generally believed to have grown from random, small-amplitude inhomogeneities, present in the early universe. We investigate how gravitational instability drives the distribution of these fluctuations away from the initial state, assumed to be Gaussian. Using second-order perturbation theory, we calculate !he skewness factor, S_3_ = <δ^3^>/<δ^2^>^2^. Here the angle brackets, <...>, denote an ensemble average, and δ is the density contrast field, smoothed with a low-pass spatial filter. We show that S_3_ decreases with the slope of the fluctuation power spectrum; it depends only weakly on {OMEGA}, the cosmological density parameter. We compare perturbative calculations with N-body experiments and find excellent agreement over a wide dynamic range. If galaxies trace the mass, measurements of S3 can be used to distinguish models with Gaussian initial conditions from their non-Gaussian alternatives.
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Juszkiewicz et al. (1993) studied this question.