We follow a low-energy effective theory approach to identify the general class of theories that describes a vector field (of unconstrained norm) coupled to gravity. The resulting set may be regarded as a generalization of the conventional vector-tensor theories, and as a high-momentum completion of aether models. We study the conditions that a viable cosmology, Newtonian limit and absence of classical and quantum instabilities impose on the parameters of our class of models, and compare these constraints with those derived in previously studied and related cases. The most stringent conditions arise from the quantum stability of the theory, which allows dynamical cosmological solutions only for a non-Maxwellian kinetic term. The gravitational constant in the Newtonian limit turns to be scale dependent, suggesting connections to dark matter and degravitation. This class of theories has a very rich gravitational phenomenology, and offers an ample but simple testing ground to study modifications of gravity and their cosmological implications.
Armendariz-Picon, Christian and Diez-Tejedor, Alberto, "Aether Unleashed" (2009). Physics. 225.
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