  In stark contrast with the three-dimensional case, higher-dimensional
Chern-Simons theories can have non-topological, propagating degrees of freedom.
Finding those vacua that allow for the propagation of linear perturbations,
however, proves to be surprisingly challenging. The simplest solutions are
somehow "hyper-stable," preventing the construction of realistic,
four-dimensional physical models.
  Here, we show that a Randall-Sundrum brane universe can be regarded as a
vacuum solution of Chern-Simons gravity in five-dimensional spacetime, with non
vanishing torsion along the dimension perpendicular to the brane. Linearized
perturbations around this solution not only exist, but behave as standard
gravitational waves on a four-dimensional Minkowski background. In the
non-perturbative regime, the solution leads to a four-dimensional "cosmological
function" $\Lambda \left( x \right)$ which depends on the Euler density of the
brane.
  Interestingly, the fact that the solution admits nontrivial linear
perturbations seems to be related to an often neglected property of the
Randall-Sundrum spacetime: that it is a group manifold, or, more precisely, two
identical group manifolds glued together along the brane. The gravitational
theory is then built around this fact, adding the Lorentz generators and one
scalar generator needed to close the algebra. In this way, a conjecture
emerges: a spacetime that is also a group manifold can be regarded as the
ground state of a Chern-Simons theory for an appropriate Lie algebra.
