Abstract
We follow an effective field theory approach to identify the general class of theories that describes a real vector field coupled to gravity at low energies, large distances and long timescales. Here we restrict ourselves to the case in which Lorentz invariance is spontaneously broken at low energies (i.e. at energies bellow the characteristic scale of the effective theory). We find the constraints on the parameter space of the theory coming from the absence of classical and quantum instabilities. We apply our results to the flat case before closing.
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