MODELING MULTI-STREAM FLOW IN COLLISIONLESS MATTER - APPROXIMATIONS FOR LARGE-SCALE STRUCTURE BEYOND SHELL-CROSSING

The generally held view that a model of large-scale structure, formed by collisionless matter in the Universe, can be based on the matter mo del ''dust'' fails in the presence of multi-stream flow, i.e., velocit y dispersion. We argue that models for large-scale structure should ra ther be constructed for a flow which describes the average motion of a multi-stream system. We present a clearcut reasoning how to approach the problem and derive an evolution equation for the mean peculiar-vel ocity relative to background solutions of Friedmann-Lemaitre type. We consider restrictions of the nonlinear problem and show that the effec t of velocity dispersion gives rise to an effective viscosity of non-d issipative gravitational origin. We discuss subcases which arise natur ally from this approach: the ''sticky particle model'' and the ''adhes ion approximation''. We also construct a novel approximation that feat ures adhesive action in the multi-stream regime while conserving momen tum, which was considered a drawback of the standard approximation bas ed on Burgers' equation. We finally argue that the assumptions made to obtain these models should be relaxed and we discuss how this can be achieved.