New kinetic interactions for massive gravity?

Claudia De Rham, Andrew Matas, Andrew J. Tolley

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


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.

Original languageEnglish (US)
Article number165004
JournalClassical and Quantum Gravity
Issue number16
StatePublished - Aug 21 2014


  • Hamiltonian analysis
  • massive gravity
  • modified gravity

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