Generalized Gravity and a Ghost

TL;DR

The paper investigates generalized gravity built from curvature invariants $F(R,R_{ab}R^{ab},R_{abcd}R^{abcd})$ and proves its equivalence to a multi-scalar-tensor theory with four derivatives. By expanding around a vacuum, it reveals a massive spin-0 mode and a massive spin-2 ghost arising from the $R^2$ and Weyl-squared terms, respectively, highlighting fundamental stability and unitarity concerns. When applied to the CDDETT model, the analysis shows tachyonic masses and a ghost, leading to vacuum instability and an inadequate Newtonian limit, thus signaling serious viability problems for these modifications. Overall, the work clarifies the field content of higher-curvature gravity and underscores the theoretical and observational challenges in using such theories as viable alternatives for dark energy or gravity modification.

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.