Generalized Gravity and a Ghost

TL;DR

This paper demonstrates that generalized gravity theories with complex curvature invariants are equivalent to multi-scalar-tensor gravities with four-derivative terms, revealing the presence of a massive ghost mode.

Contribution

It establishes the equivalence between complex curvature invariant theories and multi-scalar-tensor gravities, and analyzes the ghost modes arising in such theories.

Findings

Generalized gravity theories are equivalent to multi-scalar-tensor gravities.

A massive spin-2 ghost mode appears in these theories.

The action reduces to Einstein gravity with additional four-derivative terms.

Abstract

We show that generalized gravity theories involving the curvature invariants of the Ricci tensor and the Riemann tensor as well as the Ricci scalar are equivalent to multi- scalar-tensor gravities with four derivatives terms. By expanding the action around a vacuum spacetime, the action is reduced to that of the Einstein gravity with four derivative terms, and consequently there appears a massive spin-2 ghost in such generalized gravity theories in addition to a massive spin-0 field.