Massive Gravity Theories and limits of Ghost-free Bigravity models

Abstract

We construct a class of theories which extend New Massive Gravity to higher orders in curvature in any dimension. The lagrangians arise as limits of a new class of bimetric theories of Lovelock gravity, which are unitary theories free from the Boulware-Deser ghost. These Lovelock bigravity models represent the most general non-chiral ghost-free theories of an interacting massless and massive spin-two field in any dimension. The scaling limit is taken in such a way that unitarity is explicitly broken, but the Boulware-Deser ghost remains absent. This automatically implies the existence of a holographic $c$-theorem for these theories. We also show that the Born-Infeld extension of New Massive Gravity falls into our class of models demonstrating that this theory is also free of the Boulware-Deser ghost. These results extend existing connections between New Massive Gravity, bigravity theories, Galileon theories and holographic $c$-theorems.

11+5 pages

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• On Consistent Theories of Massive Spin-2 Fields Coupled to Gravity
• Growth Histories in Bimetric Massive Gravity
• Bimetric gravity doubly coupled to matter: theory and cosmological implications
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• Spin-2 and the Weak Gravity Conjecture
• Gravitational Waves in Ghost Free Bimetric Gravity
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Is Bimetric Gravity Really Ghost Free?
• Structures in multiple spin-2 interactions
• The Holographic c-theorem and Infinite-dimensional Lie Algebras
• Unitary Extension of Exotic Massive 3D Gravity from Bi-gravity
• Novel nonlinear kinetic terms for gravitons
• Nonlocal Massive Gravity from Einstein Gravity
• Non-linearly ghost-free higher curvature gravity
• Black Holes in Multi-Metric Gravity
• Ghost-free infinite derivative gravity
• Canonical equivalence, quantization and anisotropic inflation in higher order theory of gravity
• Holographic RG Flows from Quasi-Topological Gravity
• Towards construction of ghost-free higher derivative gravity from bigravity
• On five-dimensional massive (bi-)gravity
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• On two-vierbein gravity action from gauge theory of conformal group
• Weak field limit in vierbein-Einstein-Palatini formalism and Fierz-Pauli Equation
• Aspects of three-dimensional higher-curvature gravities