Abstract
We investigate a Lorentz invariant action which is quadratic in two rank-2 symmetric tensor fields in Minkowski spacetime. We apply a scalar-vector-tensor decomposition to two tensor fields by virtue of 3-dimensional rotation-invariance of Minkowski spacetime and classify theories with seven degrees of freedom based on the Hamiltonian analysis. We find two new theories, which cannot be mapped from the linearized Hassan-Rosen bigravity. In these theories, the new mass interactions can be allowed thanks to the transverse diffeomorphism invariance of action.
Highlights
The attempt to seek ghost-free massive gravity theories has again attracted considerable attention by the discovery of de Rham–Gabadadze–Tolley massive gravity [1]
Because of the complexity of the analysis, we only focus on theories with 7 physical degree of freedom (DOF), namely 2 × 2 ðtensorÞ þ 2 ðvectorÞ þ 1 ðscalarÞ DOFs, as in the Hassan-Rosen bigravity [19] that consists of massless and massive spin-2 fields in the linearized limit
We investigated a Lorentz invariant action for two rank-2 symmetric tensor fields hμν and fμν
Summary
The attempt to seek ghost-free massive gravity theories has again attracted considerable attention by the discovery of de Rham–Gabadadze–Tolley (dRGT) massive gravity [1]. The dRGT massive gravity possesses the cosmological constant solution in a cosmological background [9], it is perturbatively unstable [10,11] In Hassan-Rosen bigravity, the total number of physical DOFs is 7, which consists of 2 from a massless graviton and 5 from a massive graviton This fact can be seen by expanding both metrics around Minkowski spacetime, that is, gμν → ημν þ hμν=Mg and fμν → ημν þ fμν=Mf, where Mg and Mf are, respectively, the Planck mass for the metric gμν and fμν. The mixing terms between h and f in the mass terms can be removed by introducing the linear combination of two metrics,
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