  The non-perturbative curvature inhomogeneities induced by relativistic
viscous fluids are not conserved in the large-scale limit. However when the
bulk viscosity is a function of the total energy density of the plasma (or of
the trace of the extrinsic curvature) the relevant evolution equations develop
a further symmetry preventing the non-linear growth of curvature perturbations.
In this situation the fully inhomogeneous evolution can be solved to leading
order in the gradient expansion. Over large-scales both the acceleration and
the curvature inhomogeneities are determined by the bulk viscosity
coefficients. Conversely the shear viscosity does not affect the evolution of
the curvature and does not produce any acceleration. The curvature modes
analyzed here do not depend on the choice of time hypersurfaces and are
invariant for infinitesimal coordinate transformations in the perturbative
regime.
