Conditions for positivity of energy in superrenormalizable polynomial gravity

TL;DR

This paper investigates energy positivity conditions in superrenormalizable polynomial gravity models with six and eight derivatives, highlighting differences from fourth-order gravity and analyzing tensor and scalar sectors.

Contribution

It identifies conditions under which energy remains positive in higher-derivative gravity models, extending analysis beyond the tensor sector to scalar sectors.

Findings

Tensor sector energy is positively defined in UV regime.

Scalar sector energy positivity is also examined.

Higher derivatives may help control ghost effects.

Abstract

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.