Conditions for positivity of energy in superrenormalizable polynomial gravity

At the quantum level, the polynomial models of gravity with six and eight derivatives are superrenormalizable, but suffer from higher derivative ghost and/or tachyonic ghost states. On the other hand, these models may have advantages in the control of negative effects of ghosts, compared to the more common fourth-derivative theory. We explore the positiveness of energy of the individual plane wave solutions in the general models with six and eight derivatives. Different from the fourth-order gravity, the part of the energy which may be seen as the leading one in the UV, is positively defined in the tensor sector. We extend this investigation to the scalar sectors of the free theory.