  We investigate the out-of-equilibrium dynamics of viscous fluids in a
spatially flat Friedmann-Lema\^itre-Robertson-Walker cosmology using the most
general causal and stable viscous energy-momentum tensor defined at first order
in spacetime derivatives. In this new framework a pressureless viscous fluid
having density $\rho$ can evolve to an asymptotic future solution in which the
Hubble parameter approaches a constant while $\rho \rightarrow 0$, even in the
absence of a cosmological constant (i.e., $\Lambda = 0$). Thus, while viscous
effects in this model drive an accelerated expansion of the universe, the
density of the viscous component itself vanishes, leaving behind only the
acceleration. This behavior emerges as a consequence of causality in
first-order theories of relativistic fluid dynamics and it is fully consistent
with Einstein's equations.
