Beyond Lovelock gravity: Higher derivative metric theories
  We consider theories describing the dynamics of a four-dimensional metric,
whose Lagrangian is diffeomorphism invariant and depends at most on second
derivatives of the metric. Imposing degeneracy conditions we find a set of
Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or
contain more than two degrees of freedom. Among the partially degenerate
theories, we recover Chern-Simons gravity, endowed with constraints whose
structure suggests the presence of instabilities. Then, we enlarge the class of
parity violating theories of gravity by introducing new "chiral scalar-tensor
theories". Although they all raise the same concern as Chern-Simons gravity,
they can nevertheless make sense as low energy effective field theories or, by
restricting them to the unitary gauge (where the scalar field is uniform), as
Lorentz breaking theories with a parity violating sector.
