Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory

TL;DR

This paper links ghost-free bimetric theory with higher derivative gravity, including conformal gravity, revealing the nature of ghosts and the role of gauge symmetries, and proposing a ghost-free extension of conformal gravity.

Contribution

It establishes a correspondence between bimetric theory and higher derivative gravity, clarifies the nature of ghosts, and relates partially massless bimetric theory to conformal gravity.

Findings

Ghosts in higher derivative gravity are artifacts of truncation.

Partially massless bimetric theory shares equations of motion with conformal gravity.

New gauge symmetry extends Weyl symmetry, indicating a ghost-free completion.

Abstract

In this paper we establish the correspondence between ghost-free bimetric theory and a class of higher derivative gravity actions, including conformal gravity and New Massive Gravity. We also characterize the relation between the respective equations of motion and classical solutions. We illustrate that, in this framework, the spin-2 ghost of higher derivative gravity is an artifact of the truncation to a 4-derivative theory. The analysis also gives a relation between the proposed partially massless (PM) bimetric theory and conformal gravity, showing, in particular, the equivalence of their equations of motion at the 4-derivative level. For the PM bimetric theory this provides further evidence for the existence of an extra gauge symmetry and the associated loss of a propagating mode away from de Sitter backgrounds. The new symmetry is an extension of Weyl symmetry which also suggests the PM bimetric theory as a ghost-free completion of conformal gravity.