Abstract
We derive new constraints on massive gravity from unitarity and analyticity of scattering amplitudes. Our results apply to a general effective theory defined by Einstein gravity plus the leading soft diffeomorphism-breaking corrections. We calculate scattering amplitudes for all combinations of tensor, vector, and scalar polarizations. The high-energy behavior of these amplitudes prescribes a specific choice of couplings that ameliorates the ultraviolet cutoff, in agreement with existing literature. We then derive consistency conditions from analytic dispersion relations, which dictate positivity of certain combinations of parameters appearing in the forward scattering amplitudes. These constraints exclude all but a small island in the parameter space of ghost-free massive gravity. While the theory of the "Galileon" scalar mode alone is known to be inconsistent with positivity constraints, this is remedied in the full massive gravity theory.
Highlights
After an intensive computation, we arrive at lengthy expressions for the general treelevel amplitude for the scattering of massive gravitons
We have calculated the massive graviton scattering amplitude at general kinematics using the above definitions of the external polarization tensors, together with the Feynman rules extracted from eq (2.2) after going to canonical normalization where hμν is rescaled by mPl/2
We present f and map the positivity bound from analytic dispersion relations onto the parameter space of massive gravity
Summary
We consider a general effective theory for massive gravity defined by the Einstein-Hilbert term plus soft diffeomorphism-breaking operators [1]. This starting point is familiar from other contexts, e.g., soft breaking of gauge symmetry or supersymmetry. Boulware and Deser [8] observed that a dangerous ghost degree of freedom is reintroduced in non-trivial backgrounds. It was observed that the Boulware-Deser ghost can be eliminated with the proper choice of parameters [3, 4, 9]. The theory enjoys a parametrically higher cutoff Λ3 [2, 3], since the parameter choice eliminates dangerous scalar self-interactions
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