Lagrangian Dynamics in Non-Flat Universes and Non-Linear Gravitational Evolution

Details Lagrangian Dynamics in Non-Flat Universes and Non-Linear Gravitational Evolution Lagrangian Dynamics in Non-Flat Universes and Non-Linear Gravitational Evolution

1994-06-07

arxiv.org/abs/astro-ph/9406016v3

Mon.Not.Roy.Astron.Soc.276:115,1995

Astronomy and Astrophysics

Astrophysics

30 pages, Latex, revised version (two appendices are added), to be published in Monthly Notices of the Royal Astronomical Soci

Scientific paper

We present a new formalism which allows to derive the general Lagrangian dynamical equations for the motion of gravitating particles in a non--flat Friedmann universe with arbitrary density parameter $\Omega$ and no cosmological constant. We treat the set of particles as a Newtonian collisionless fluid. The non--linear dynamical evolution of the fluid element trajectories is then described up to the third--order expansion in Lagrangian coordinates. This work generalizes recent investigations carried out by Bouchet \etal (1992) and Buchert (1994).

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