Abstract
We revisit and extend the `Effective field theory for massive gravitons' constructed by Arkani-Hamed, Georgi and Schwartz in the light of recent progress in constructing ghost-free theories with multiple interacting spin-2 fields. We show that there exist several dual ways of restoring gauge invariance in such multi-gravity theories, find a generalised Fierz-Pauli tuning condition relevant in this context and highlight subtleties in demixing tensor and scalar modes. The generic multi-gravity feature of scalar mixing and its consequences for higher order interactions are discussed. In particular we show how the decoupling limit is qualitatively changed in theories of interacting spin-2 fields. We relate this to dRGT (de Rham, Gabadadze, Tolley) massive gravity, Hassan-Rosen bigravity and the multi-gravity constructions by Hinterbichler and Rosen. As an additional application we show that EBI (Eddington-Born-Infeld) bigravity and higher order generalisations thereof possess ghost-like instabilities.
Highlights
Massive gravity has recently experienced a remarkable renaissance
Summary so far: Until now we have reviewed the construction of [77] to introduce and use Stuckelberg fields in order to restore gauge invariances broken by bimetric interaction terms
This effectively projects out the n − 1 Goldstone modes of the n − 1 GC(i) symmetries broken by the interaction terms and which got eaten to produce n − 1 massive ‘gravitons’ in the initial gauge-fixed action
Summary
Massive gravity has recently experienced a remarkable renaissance. While at the linearised level the Fierz-Pauli action [1] has long been known to consistently describe a single massive spin-2 field, any concrete fully non-linear extension/deformation of general relativity (GR) designed to give the graviton a mass appeared to inevitably run into problems [2,3,4,5,6,7,8]. In this paper we endeavour to complete this effective field theory picture by constructing what we dub an ‘Effective field theory for interacting spin-2 fields’ This means we extend and generalise the ‘Effective field theory for massive gravitons’ by [77] to deal with generic (i.e. non Fierz-Pauli) N-metric interaction terms – especially relevant in the light of the afore-mentioned progress in massive/multi-gravity – and general combinations of interaction terms as discussed by [71] rather than restricting ourselves to purely nearest-neighbour interactions as in [77]. Some further useful results are collected in appendices A, B and C
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