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 the skewness factor, $S_3 equiv langle delta^3 angle , /, langle delta^2 angle^2$. Here the brackets, $langle ldots angle$, denote an ensemble average, and $delta$ 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 $S_3$ can be used to distinguish models with Gaussian initial conditions from their non-Gaussian alternatives.