  A description of many-particle systems, which is more fundamental than the
fluid approach, is to consider them as a kinetic gas. In this approach the
dynamical variable in which the properties of the system are encoded, is the
distribution of the gas particles in position and velocity space, called
1-particle distribution function (1PDF). However, when the gravitational field
of a kinetic gas is derived via the Einstein-Vlasov equations, the information
about the velocity distribution of the gas particles is averaged out and
therefore lost. We propose to derive the gravitational field of a kinetic gas
directly from its 1PDF, taking the velocity distribution fully into account. We
conjecture that this refined approach could possibly account for the observed
dark energy phenomenology.
