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

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Department of Physics & The Oskar Klein Centre, Stockholm University, AlbaNova University Centre, SE-106-91 Stockholm, Sweden
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Institut für Theoretische Physik, Eidgenössische Technische Hochschule Zürich Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland
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UPMC-CNRS, UMR7095, Institut d'Astrophysique de Paris, GReCO, 98bis boulevard Arago, F-75014 Paris, France
*
Author to whom correspondence should be addressed.
Academic Editors: Kazuharu Bamba and Sergei D. Odintsov
Universe 2015, 1(2), 92-122; https://doi.org/10.3390/universe1020092
Received: 12 May 2015 / Revised: 8 July 2015 / Accepted: 9 July 2015 / Published: 20 July 2015
(This article belongs to the Special Issue Modified Gravity Cosmology: From Inflation to Dark Energy)
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. View Full-Text
Keywords: modified gravity; higher spin fields; conformal gravity modified gravity; higher spin fields; conformal gravity
MDPI and ACS Style

Hassan, S.F.; Schmidt-May, A.; Von Strauss, M. Higher Derivative Gravity and Conformal Gravity from Bimetric and Partially Massless Bimetric Theory. Universe 2015, 1, 92-122. https://doi.org/10.3390/universe1020092

AMA Style

Hassan SF, Schmidt-May A, Von Strauss M. Higher Derivative Gravity and Conformal Gravity from Bimetric and Partially Massless Bimetric Theory. Universe. 2015; 1(2):92-122. https://doi.org/10.3390/universe1020092

Chicago/Turabian Style

Hassan, Sayed F., Angnis Schmidt-May, and Mikael Von Strauss. 2015. "Higher Derivative Gravity and Conformal Gravity from Bimetric and Partially Massless Bimetric Theory" Universe 1, no. 2: 92-122. https://doi.org/10.3390/universe1020092

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