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The cuscuton is a scalar field with infinite speed of propagation. It was introduced in the context of cosmology but it has also been claimed to resemble Ho r rava gravity in a certain limit. Here we revisit the cuscuton theory as a Lorentz-violating gravity theory. We clarify its relation with Ho r rava gravity and Einstein-ther theory, analyze its causal structure, and consider its initial value formulation. Finally, we discuss to which extent the cuscuton theory can be used as a proxy for Ho r rava gravity in the context of gravitational collapse and formation of universal horizons.
Bhattacharyya et al. (Tue,) studied this question.