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 exactly, rather than approximately, even for cosmological models with arbitrary density parameter Omega. The Eulerian approach we present here allows us 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.

Eulerian Perturbation Theory in Non-Flat Universes: Second Order Approximation

LUCCHIN, FRANCESCO;MATARRESE, SABINO;MOSCARDINI, LAURO
1995

Abstract

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 exactly, rather than approximately, even for cosmological models with arbitrary density parameter Omega. The Eulerian approach we present here allows us 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/135881
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