Abstract
Massive gravity (mGR) describes a dynamical “metric” on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its “mean field theory”. Analyzing mean field massive gravity (m‾GR) propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita–Schwinger (RS) theory. The fiducial and mGR mean field background metrics in the m‾GR model correspond to the RS Minkowski metric and external EM field. The common implications in both systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories; a situation in stark contrast with general relativity (GR) which is at least a consistent classical theory. Moreover, even though both m‾GR and RS theories can still in principle be considered as predictive effective models in the weak regime, their lower helicities then exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. Thus our approach has uncovered a novel, dispersive, “crystal-like” phenomenon of differing helicities having differing propagation speeds. This applies both to m‾GR and mGR, and is a peculiar feature that is also problematic for consistent coupling to matter.
Highlights
Consistency is a powerful tool for studying field theories
Models whose constraints do not single out the correct propagating degree of freedom (DoF) suffer from relatively ghost kinetic terms: the relevant example here is the sixth ghost excitation that plagues generic massive gravity theories [1]
In previous works we and other authors have shown that similar conclusions hold for the full non-linear massive gravity (mGR) models [5, 6, 13, 14, 7, 15]
Summary
Consistency is a powerful tool for studying field theories. Already classically, there are stringent conditions that are extremely difficult to fulfill for systems with spin s > 1, the most important exception being (s = 2, m = 0) general relativity (GR). In previous works we and other authors have shown that similar conclusions hold for the full non-linear mGR models [5, 6, 13, 14, 7, 15] These investigations rely on the method of characteristics, which amounts to studying leading kinetic terms and is essentially equivalent to an analysis of linear fluctuations around a mean field background. Since this mean field massive gravity (mGR) fluctuation model depends both on a background and a fiducial metric, it is in direct correspondence with the charged RS model. Apart from confirming earlier conclusions in a very simple setting, our results give a precise description of mGR’s effective, weak field, regime
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