Hydrodynamic Attractor of a Viscous Fluid in an Expanding Universe

The Israel-Stewart theory of relativistic hydrodynamics is a prominent tool often used to study heavy ion collisions and, under certain conditions, has been shown to be causal and well-posed when coupled to gravity. We study an Israel-Stewart theory of relativistic fluids with bulk viscosity coupled to Einstein's equations in a Friedmann-Lemaître-Robertson-Walker (FLRW) expanding universe. Solutions to these equations are found to converge to two attractors corresponding toearly times and late times. We perform a numerical analysis of these attractors and compare theresults to an analytical solution found using a slow roll approximation. The fluid is found to reach a stable out of equilibrium value as the universe tends to a fixed rate of expansion.