  In this paper, I present the calculation of the third and fourth moments of
both the distribution function of the large--scale density and the large--scale
divergence of the velocity field, $\theta$. These calculations are made by the
mean of perturbative calculations assuming Gaussian initial conditions and are
expected to be valid in the linear or quasi linear regime. The moments are
derived for a top--hat window function and for any cosmological parameters
$\Omega$ and $\Lambda$. It turns out that the dependence with $\Lambda$ is
always very weak whereas the moments of the distribution function of the
divergence are strongly dependent on $\Omega$. A method to measure $\Omega$
using the skewness of this field has already been presented by Bernardeau et
al. (1993). I show here that the simultaneous measurement of the skewness and
the kurtosis allows to test the validity of the gravitational instability
scenario hypothesis. Indeed there is a combination of the first three moments
of $\theta$ that is almost independent of the cosmological parameters $\Omega$
and $\Lambda$, $${(<\theta^4>-3<\theta^2>^2) <\theta^2> \over
<\theta^3>^2}\approx 1.5,$$ (the value quoted is valid when the index of the
power spectrum at the filtering scale is close to -1) so that any cosmic
velocity field created by gravitational instabilities should verify such a
property.
