  We review the evolution of a spatially homogeneous and isotropic universe
described by a Friedmann-Robertson-Walker spacetime filled with a
collisionless, neutral, simple, massive gas. The gas is described by a
one-particle distribution function which satisfies the Liouville equation and
is assumed to be homogeneous and isotropic. Making use of the isometries of the
spacetime, we define precisely the homogeneity and isotropicity property of the
distribution function, and based on this definition we give a concise
derivation of the most general family of such distribution functions. For this
family, we construct the particle current density and the stress-energy tensor
and consider the coupled Einstein-Liouville system of equations. We find that
as long as the distribution function is collisionless, homogenous and
isotropic, the evolution of a Friedmann-Robertson-Walker universe exhibits a
singular origin. Its future development depends upon the curvature of the
spatial sections: spatially flat or hyperboloid universes expand forever and
this expansion dilutes the energy density and pressure of the gas, while a
universe with compact spherical sections reaches a maximal expansion, after
which it reverses its motion and recollapses to a final crunch singularity
where the energy density and isotropic pressure diverge. Finally, we analyze
the evolution of the universe filled with the collisionless gas once a
cosmological constant is included.
