Astronomy and Astrophysics – Astrophysics
Scientific paper
1994-11-16
Mon.Not.Roy.Astron.Soc.276:39,1995
Astronomy and Astrophysics
Astrophysics
17 pages, Latex (mn.sty), 1 figure, revised version (1 figure is dropped; eq.46 is corrected and some consequent results are r
Scientific paper
The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved {\it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter $\Omega$. The Eulerian approach we present here allows to calculate the higher-order moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocity-divergence fields for any value of $\Omega$, confirming the extremely weak $\Omega$-dependence of the skewness previously obtained via Lagrangian perturbation theory. Our results show that the separability assumption of higher-order Eulerian perturbative solutions is restricted to the Einstein-de Sitter case only.
Catelan Paolo
Lucchin Francesco
Matarrese Sabino
Moscardini Lauro
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