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 at the linear level is an artifact of the truncation to a four-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 four-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 invariance, which may suggest the candidate PM bimetric theory as a possible ghost-free completion of conformal gravity.
Highlights
We show the correspondence between the ghost-free bimetric theory [1,2] and higher derivative gravity, both of which have similar spectra, but only the bimetric case is ghost-free
This implies a close relation between conformal gravity and a specific bimetric theory that has been proposed [3,4] as the sought-after nonlinear partially massless (PM) theory
R(g) < m2, in special cases, the series terminates and the solution is exact. Using this solution to eliminate fμν from the bimetric action, we obtain the action for higher derivative gravity as, S HD [g] = S[g, f (g)]
Summary
We show the correspondence between the ghost-free bimetric theory [1,2] and higher derivative gravity, both of which have similar spectra, but only the bimetric case is ghost-free. This implies a close relation between conformal gravity and a specific bimetric theory that has been proposed [3,4] as the sought-after nonlinear partially massless (PM) theory. We start with a brief discussion of various theories considered in this paper, emphasizing the features that are of relevance here. A scalar field example is worked out in Appendix A, and some calculational details are relegated to Appendix B
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
