  We study a metric cubic gravity theory considering odd-parity modes of linear
inhomogeneous perturbations on a spatially homogeneous Bianchi type I manifold
close to the isotropic de Sitter spacetime. We show that in the regime of small
anisotropy, the theory possesses new degrees of freedom compared to General
Relativity, whose kinetic energy vanishes in the limit of exact isotropy. From
the mass dispersion relation we show that such theory always possesses at least
one ghost mode as well as a very short-time-scale (compared to the Hubble time)
classical tachyonic (or ghost-tachyonic) instability. In order to confirm our
analytic analysis, we also solve the equations of motion numerically and we
find that this instability is developed well before a single e-fold of the
scale factor. This shows that this gravity theory, as it is, cannot be used to
construct viable cosmological models.
