  We investigate the stability against inhomogeneous perturbations and the
appearance of ghost modes in Gauss-Bonnet gravitational theories with a
non-minimally coupled scalar field, which can be regarded as either the dilaton
or a compactification modulus in the context of string theory. Through
cosmological linear perturbations we extract four no-ghost and two sub-luminal
constraint equations, written in terms of background quantities, which must be
satisfied for consistency. We also argue that, for a general action with
quadratic Riemann invariants, homogeneous and inhomogeneous perturbations are,
in general, inequivalent, and that attractors in the phase space can have
ghosts. These results are then generalized to a two-field configuration.
Single-field models as candidates for dark energy are explored numerically and
severe bounds on the parameter space of initial conditions are placed. A number
of cases proposed in the literature are tested and most of them are found to be
unstable or observationally unviable.
