Positive signs in massive gravity

By C. Cheung, Grant N. Remmen. 2016

134 citations recorded by the source corpus.

A bstractWe 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ef95c530c3e18df194f39b6afeee37df0f076966

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Citations in the corpus

UV complete me: positivity bounds for particles with spin (2017, background): “For example, this has been shown to severely constrain the parameter space of massive gravity [7], and pseudo-linear massive gravity [8].”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “This was performed in [143, 144, 145] and we refer the reader to them for a more detailed discussion.”
Extremal effective field theories (2020, result): “The relation between dimensional analysis scaling and causality resonates with many previous studies, for example [2–6].”
New positivity bounds from full crossing symmetry (2020, background): “Recently, there has been a lot of interest in applying the positivity bounds in particle physics, gravitational theories and cosmology [17–39].”
Softness and amplitudes’ positivity for spinning particles (2016, background): “for the theory of massive gravity where the leading Galileon mode scales as O(p6) while the sub-leading contributions go like m(2)gp 4/Λ6 [16] and ΛIR is identified with the graviton mass mg.”