Skewness induced by gravity

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, S₃_ = /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 S₃_ 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.