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

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...

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Bibliographic Details
Published in:Universe (Basel) 2015-09, Vol.1 (2), p.92-122
Main Authors: Hassan, Sayed, Schmidt-May, Angnis, Von Strauss, Mikael
Format: Article
Language:English
Subjects:
conformal gravity
Energy
Gravity
higher spin fields
modified gravity
Theory of relativity
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Summary: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.
ISSN:2218-1997
2218-1997
DOI:10.3390/universe1020092