Eulerian perturbation theory in nonflat universes: secondorder approximation
Abstract
The problem of solving perturbatively the equations describing the evolution of selfgravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved exactly, rather than approximately, even for cosmological models with arbitrary density parameter Omega. The Eulerian approach we present here allows us to calculate the higherorder moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocitydivergence fields for any value of Omega, confirming the extremely weak Omegadependence of the skewness previously obtained via Lagrangian perturbation theory. Our results show that the separability assumption of higherorder Eulerian perturbative solutions is restricted to the Einsteinde Sitter case only.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 1995
 DOI:
 10.1093/mnras/276.1.39
 arXiv:
 arXiv:astroph/9411066
 Bibcode:
 1995MNRAS.276...39C
 Keywords:

 GRAVITATION;
 GALAXIES: GENERAL;
 COSMOLOGY: THEORY;
 LARGESCALE STRUCTURE OF UNIVERSE;
 Astrophysics
 EPrint:
 17 pages, Latex (mn.sty), 1 figure, revised version (1 figure is dropped