  The study of linear perturbation theory for general functions of the Ricci
and Gauss-Bonnet scalars is done over an empty anisotropic universe, i.e. the
Kasner-type background, in order to show that an anisotropic background in
general has ghost degrees of freedom, which are absent on
Friedmann-Lemaitre-Robertson-Walker (FLRW) backgrounds. The study of the scalar
perturbation reveals that on this background the number of independent
propagating degrees of freedom is four and reduces to three on FLRW
backgrounds, as one mode becomes highly massive to decouple from the physical
spectrum. When this mode remains physical, there is inevitably a ghost mode.
