## 6. ConclusionThus, in this article we have developed a simple model for
hierarchical clustering based on a spherical dynamics. We have shown
it provides a reasonable approximation to the density field, and the
divergence of the velocity field, in the quasi-linear regime
. Moreover, it allows one to recover the exact
series of the moments of the probability distribution of the density
contrast in the limit (contrary to other models
like the Zeldovich approximation for instance), and sheds some light
on the rigorous results. Then, we have developed a way to extend this
model into the non-linear regime, by taking into account the
virialization of high overdensities (as in the PS approach) and also
the behaviour of very underdense areas (in a way different from the PS
prescription). This implies a particular scaling in © European Southern Observatory (ESO) 1998 Online publication: August 27, 1998 |