Relativistic fluids in cosmological spacetimes

We review the status of mathematical research on the dynamical properties of relativistic fluids in cosmological spacetimes-both, in the presence of gravitational backreaction as well as the evolution on fixed cosmological backgrounds. We focus in particular on the phenomenon of fluid stabilization, which describes the taming effect of spacetime expansion on the fluid. While fluids are in general known to form shocks from regular initial data, spacetime expansion has been found to suppress this behaviour. During the last decade, various rigorous results on this problem have been put forward. We review these results, the mathematical methods involved and provide an outlook on open questions.