  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
Horava gravity in a certain limit. Here we revisit the cuscuton theory as a
Lorentz-violating gravity theory. We clarify its relation with Horava gravity
and Einstein-aether 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 Horava gravity in the context of
gravitational collapse and formation of universal horizons.
