D. Comelli, M. Crisostomi, F. Nesti, L. Pilo
We study in a systematic way a generic massive deformation of general relativity using the Hamiltonian formalism. The number of propagating degrees of freedom is determined in a non-perturbative and background independent way. We show that the condition of having only five propagating degrees of freedom can be cast in a differential equation for the deforming potential whose solutions produce a number of candidates both in the Lorentz invariant and in Lorentz breaking case. In the Lorentz invariant case we recover the known ghost-free solutions, which in the massless limit matches General Relativity non perturbatively through the Vainshtein mechanism. We argue that a more interesting Lorentz-breaking theory of massive gravity free from ghosts in Minkowski space and without the vDVZ discontinuity can be defined. This is thus a step forward to a viable weakly coupled and calculable large distance modification of gravity.
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http://arxiv.org/abs/1204.1027
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