Bi-gravity with a single graviton

Sergey Alexandrov (1) , Simone Speziale (2, 3)

1 L2C - Laboratoire Charles Coulomb
2 CPT - Centre de Physique Théorique - UMR 7332
3 CPT - E4 Gravité quantique

We analyze a bi-gravity model based on the first order formalism, having as fundamental variables two tetrads but only one Lorentz connection. We show that on a large class of backgrounds its linearization agrees with general relativity. At the non-linear level, additional degrees of freedom appear, and we reveal the mechanism hiding them around the special backgrounds. We further argue that they do not contain a massive graviton, nor the Boulware-Deser ghost. The model thus propagates only one graviton, whereas the nature of the additional degrees of freedom remains to be investigated. We also present a foliation-preserving deformation of the model, which keeps all symmetries except time diffeomorphisms and has three degrees of freedom.

Mots clés: Classical Theories of Gravity; Cosmology of Theories beyond the SM

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Relativité Générale et Cosmologie Quantique [gr-qc]

Sergey Alexandrov, Simone Speziale. Bi-gravity with a single graviton. Journal of High Energy Physics, 2019, 8, pp.070. ⟨10.1007/JHEP08(2019)070⟩. ⟨hal-02114493⟩