Abstract
We propose a simple method for deriving the constraints of the de Rham-Gabadadze-Tolley model in the metric and the Lagrangian formulation, as possible as keeping the Lorentz covariance. In our formulation, it is not necessary to use the Hamilton analysis, the vielbein formulation, nor the Stuckelberg trick for showing the Boulwer-Deser ghost-freeness. It realizes the Lorentz covariant expressions of the constraints in a certain parameter region.
Highlights
In a last decade, the understanding of the massive spintwo field has been quite developed
We have shown the existence of an additional constraint of the de Rham-Gabadadze-Tolley (dRGT) model in the Lagrangian formulation with the metric formulation
We found an identity (57) which plays a crucial role for the existence of the additional constraint, and we have proved the identity for any dRGT potential terms
Summary
The understanding of the massive spintwo field has been quite developed. In [5], de Rham and Gabadadze tried to tune the parameters in the massive gravity model (2) by requiring the ghostfreeness in the high-energy limit called the decoupling limit They concluded that the Lorentz covariant potential term Vðg; ηÞ consistent with this requirement is parametrized by only three free parameters (mass parameter, and other two dimensionless parameters) in D 1⁄4 4. We should note that the special tuning of the potential term in the dRGT model (4) is not essential for the existence of the constraint (16). The special tuning of the potential terms in the dRGT model (4) is essential for the existence of an additional constraint corresponding to h 1⁄4 0 in (1). The covariant expression of this constraint has not been obtained and it is the purpose in this paper
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