Thermodynamics and dynamics of a 1-D gravitational system

Aims.The dynamics of large-scale structure formation in the universe by gravitational instability still presents many open issues and is mostly studied through numerical simulations. This motivates the study of simpler models which can be investigated by analytical means in order to understand the main processes at work. Thus, we describe here a one-dimensional self-gravitating system derived from the cosmological context, which leads to an effective external potential in addition to the standard gravitational self-interaction. As a first step we consider small times so that the expansion can be neglected. Then we present a thermodynamical analysis of this system as well as the stability properties of the associated hydrodynamical and collisionless systems.