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Gravitational Properties of the Proca Field
We study various properties of a Proca field coupled to gravity through
minimal and quadrupole interactions, described by a two-parameter family of
Lagrangians. St\"uckelberg decomposition of the effective theory spells out its
model-dependent ultraviolet cutoff, parametrically larger than the Proca mass.
We present pp-wave solutions that the model admits, consider linear
fluctuations on such backgrounds, and thereby constrain the parameter space of
the theory by requiring null-energy condition and the absence of negative time
delays in high-energy scattering. We briefly discuss the positivity
constraintsderived from unitarity and analyticity of scattering
amplitudesthat become ineffective in this regard.Comment: 23 pages, revised positivity-bound analysis, references adde