  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, $S_3 \equiv
\langle \delta^3 \rangle \, /\, \langle \delta^2 \rangle^2$. Here the brackets,
$\langle \ldots \rangle$, 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.

Astrophysics