  In this work, we analyze a gravity model with higher derivatives including a
CPT-even Lorentz-violating term. In principle, the model could be a low-energy
limit of a Lorentz-invariant theory presenting the violation of Lorentz
symmetry as a consequence of a spontaneous symmetry-breaking mechanism if a
decoupling between the metric and the Nambu-Goldstone modes is assumed. We have
set up a convenient operator basis for the expansion of wave operators for
symmetric second-rank tensors in the presence of a background vector. By using
this set of operators, the particle content is obtained, and its consistency,
regarding the conditions for stability and unitarity, is discussed. We conclude
that this extra Lorentz noninvariant contribution is unable to address the
problems of stability and unitarity of higher-derivative gravity models.
