Quadratic curvature gravity on Einstein manifolds decouples into massless and non-Fierz-Pauli massive gravity sectors, enabling observational constraints on its parameters with noted tension for the Weyl term.
Hamiltonian analysis of curvature-squared gravity with or without conformal invariance
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abstract
We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable -- a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.
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representative citing papers
Symmetric teleparallel gravity has the same number of degrees of freedom as general relativity, confirmed via its Hamiltonian formulation after deriving generalized extrinsic geometry relations.
Godel and Godel-type metrics satisfy the curvature-squared field equations as causal solutions with all Weyl tensor contributions removed, while an axially symmetric metric shows Weyl-dependent modifications to energy density and the weak energy condition.
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Non-Fierz-Pauli bimetric theory from quadratic curvature gravity on Einstein manifolds
Quadratic curvature gravity on Einstein manifolds decouples into massless and non-Fierz-Pauli massive gravity sectors, enabling observational constraints on its parameters with noted tension for the Weyl term.
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Extrinsic geometry and Hamiltonian analysis of symmetric teleparallel gravity
Symmetric teleparallel gravity has the same number of degrees of freedom as general relativity, confirmed via its Hamiltonian formulation after deriving generalized extrinsic geometry relations.
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Causality Violating Solutions in Curvature-Squared Gravity
Godel and Godel-type metrics satisfy the curvature-squared field equations as causal solutions with all Weyl tensor contributions removed, while an axially symmetric metric shows Weyl-dependent modifications to energy density and the weak energy condition.
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