Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity

By Sayed Fawad Hassan, Rachel A Rosen. 2011

430 citations recorded by the source corpus.

A bstractIn massive gravity and in bimetric theories of gravity, two constraints are needed to eliminate the two phase-space degrees of freedom of the Boulware-Deser ghost. For recently proposed non-linear theories, a Hamiltonian constraint has been shown to exist and an associated secondary constraint was argued to arise as well. In this paper we explicitly demonstrate the existence of the secondary constraint. Thus the Boulware-Deser ghost is completely absent from these non-linear massive gravity theories and from the corresponding bimetric theories. Equivalently, this proves the existence of classically ghost-free theories of massive spin-2 fields, in both fixed and dynamical gravitational backgrounds.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Oceanography

View Paper: https://www.semanticscholar.org/paper/f0040b566f45f14e0252135d011473962363f328

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Citations in the corpus

Bimetric gravity is cosmologically viable (2015, background): “Recently a particular bimetric theory (or bigravity) has been shown to avoid this ghost instability [4, 5].”
Interacting spin-2 fields (2012, background): “This leads to a secondary constraint [11] which, together with the primary constraint, forms a second class pair of constraints.”
Cosmological stability bound in massive gravity and bigravity (2013, background): “3 Generalizing the Bound to Bigravity The action for bigravity models which are free from the Boulware-Deser ghost is a simple extension of that for massive gravity [11] S = ∫ d(4)x 1 2 [”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “This constitutes a second class constraint {C1, C2} 6= 0 since there is not any gauge symmetry anymore and it removes only one physical degree of freedom (see [32, 33, 136, 34, 137] for more details).”
Accelerated expansion from ghost-free bigravity: a statistical analysis with improved generality (2012, methodology): “A generalization to having two free and dynamic metrics in the formulation was then proposed and showed a theoretically viable option by Hassan and Rosen in [29, 30, 31].”
Massive Gravity (2014, methodology): “By now the confusion has been clarified, and see for instance [295, 294, 400, 346, 343, 297, 15, 259] for thorough proofs addressing all the issues raised in the previous literature.”