New Kinetic Interactions for Massive Gravity?

Abstract

We show that there can be no new Lorentz invariant kinetic interactions free from the Boulware-Deser ghost in four dimensions in the metric formulation of gravity, beyond the standard Einstein-Hilbert, up to total derivatives. We use dimensional deconstruction as a way to motivate a non-linear ansatz for potential new ghost free kinetic interactions for massive gravity, bi-gravity and multi-gravity in four and higher dimensions. These interactions descend from Lovelock terms, and so naively one might expect the interactions to be ghost free. However we show that these new interactions inevitably lead to more than five propagating degrees of freedom. We then perform a general perturbative analysis in four dimensions, and show that the only term with two derivatives that does not introduce a ghost is the Einstein-Hilbert term. This result extends to all orders in perturbations.

version published in CQG

References in corpus (6)

• Resummation of Massive Gravity
• Massive Gravity
• Acausality of Massive Gravity
• Non-Renormalization and Naturalness in a Class of Scalar-Tensor Theories
• Gravitational- and Self- Coupling of Partially Massless Spin 2
• On ghosts in theories of self-interacting massive spin-2 particles

Cited by in corpus (58)

• Beyond the Cosmological Standard Model
• Massive Gravity
• Generalization of the Proca Action
• Graviton Mass Bounds
• Ghosts & Matter Couplings in Massive (bi-&multi-)Gravity
• General Teleparallel Quadratic Gravity
• Ostrogradsky in Theories with Multiple Fields
• Cosmology of the proxy theory to massive gravity
• The coupling to matter in Massive, Bi- and Multi-Gravity
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Bounds on Amplitudes in Effective Theories with Massive Spinning Particles
• Non-linear extension of non-metricity scalar for MOND
• Linear growth of structure in massive bigravity
• Vielbein to the Rescue?
• Mild bounds on bigravity from primordial gravitational waves
• Probing the inflationary particle content: extra spin-2 field
• More on effective composite metrics
• Covariant Approach to the No-ghost Theorem in Massive Gravity
• Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields
• Field redefinitions in theories beyond Einstein gravity using the language of differential forms
• Lovelock gravities from Born-Infeld gravity theory
• Einstein Gravity, Massive Gravity, Multi-Gravity and Nonlinear Realizations
• New massive bigravity cosmologies with double matter coupling
• On the (A)dS Decoupling Limits of Massive Gravity
• Extracting Bigravity from String Theory
• The decoupling limit of Multi-Gravity: Multi-Galileons, Dualities and More
• TDiff and Weyl Invariant Massive Spin-2: Linear Theory
• Massive gravity with non-minimal coupling
• A general theory of linear cosmological perturbations: bimetric theories
• Cutoff for Extensions of Massive Gravity and Bi-Gravity
• Mass - radius ratio bounds for compact objects in Lorentz-violating dRGT Massive Gravity theory
• On nonlocally interacting metrics, and a simple proposal for cosmic acceleration
• Coupling between Galileon and massive gravity with composite metrics
• Derivative interactions for a spin-2 field at cubic order
• EFT of Interacting Spin-2 Fields
• Post-Newtonian parameter $\gamma$ and the deflection of light in ghost-free massive bimetric gravity
• On Consistent Kinetic and Derivative Interactions for Gravitons
• Gauged Galileons
• Interactions of Charged Spin-2 Fields
• Metamorphosis of the Cosmological Constant and 5D Origin of the Fiducial Metric
• New massive spin two model on curved space-time
• Novel nonlinear kinetic terms for gravitons
• Generalising the matter coupling in massive gravity: a search for new interactions
• Black Holes in Multi-Metric Gravity
• On the absence of the Boulware-Deser ghost in novel graviton kinetic terms
• A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
• Bi-gravity with a single graviton
• On Lorentz-invariant spin-2 theories
• Effective Spin-2 Quasi-particles at Linear Dispersive Five-fold Degenerate Points with Tunable Topological Chern Numbers
• On Lorentz-invariant bi-spin-2 theories
• Embeddings of the "New Massive Gravity"
• Possible Derivative Interactions in Massive bi-Gravity
• $\gamma$-ray emission signals in the massive graviton mediated dark matter model
• Nonlocal Galileons and Self-Acceleration
• Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion
• Fundamental fields around compact objects: Massive spin-2 fields, Superradiant instabilities and Stars with dark matter cores
• New cosmological solutions in massive gravity theory
• Self-interacting charged massive spin two particles in Minkowski spacetime