On the Ghost Problem of Conformal Gravity

Abstract

We study the metric perturbations around the de Sitter and Minkowski backgrounds in Conformal Gravity. We confirm the presence of ghosts in both cases. In the de Sitter case, by applying the Maldacena boundary conditions - the Neumann boundary condition and the positive-frequency mode condition - to the metric, we show that one cannot recover a general solution for the perturbations. In turn, alongside the Neumann boundary condition, we derive an additional condition with which the perturbations of conformal gravity and dS perturbations of Einstein gravity with cosmological constant coincide. We further show that the Neumann boundary condition does not lead to a general solution in Minkowski space. Conversely, we derive the alternative boundary conditions, with which we attain an agreement between the perturbations of conformal and Einstein gravity in full generality, thus removing the ghost of conformal gravity.

arXiv comment24 pages

References in corpus (30)

• The Spectral Action Principle
• D=4 Super Yang Mills, D=5 gauged supergravity and D=4 conformal supergravity
• Conformal Supergravity in Twistor-String Theory
• Aspects of Quadratic Gravity
• AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities
• A class of elementary particle models without any adjustable real parameters
• Topological regularization and self-duality in four-dimensional anti-de Sitter gravity
• Conformal Gravity and Extensions of Critical Gravity
• New Energy Definition for Higher Curvature Gravities
• From conformal to Einstein Gravity
• Conformal gravity holography in four dimensions
• Photon regions, shadow observables and constraints from M87* of a charged rotating black hole
• N=1 and N=2 pure supergravities on a manifold with boundary
• Counterterms, Kounterterms, and the variational problem in AdS gravity
• Galactic rotation curves in conformal gravity
• Charged Rotating AdS Black Hole and Its Thermodynamics in Conformal Gravity
• Einstein Gravity from Conformal Gravity in 6D
• Aspects of Weyl Supergravity
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Counterterms, critical gravity and holography
• Quasinormal modes of black holes in Weyl gravity: Electromagnetic and gravitational perturbations
• Self-Dual Conformal Gravity
• Conformal renormalization of scalar-tensor theories
• Conformal gravity does not predict flat galaxy rotation curves
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Self-dual Gravitational Instantons in Conformal Gravity: Conserved Charges and Thermodynamics
• Bimetric, Conformal Supergravity and its Superstring Embedding
• Conformal gravity with totally antisymmetric torsion
• Massive Gravity from Higher Derivative Gravity with Boundary Conditions
• Masking singularities in Weyl gravity and Ricci flows

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• Inhomogeneous metrics on complex bundles in Lovelock gravity
• Ultraviolet Completion of the Big Bang in Quadratic Gravity
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