Degenerate Hořava gravity

Horava gravity breaks Lorentz symmetry by introducing a dynamical timelike scalar field (the khronon), which can be used as preferred time coordinate (thus selecting space-time foliation). Adopting the khronon coordinate, theory is invariant only under reparametrizations and spatial diffeomorphisms. In infrared limit, this sometimes referred to khronometric theory. Here, we explicitly construct generalization of theory, avoids propagation Ostrogradski modes result suitable degeneracy condition (although stability latter radiative corrections remains an open question). While new does not have general-relativistic limit yield Friedmann-Robertson-Walker-like cosmology on large scales, it still passes, for choices its coupling constants, local tests Earth in solar system, well gravitational-wave tests. We also comment possible usefulness toy model quantum gravity, could completed ultraviolet into 'degenerate gravity' that perturbatively renormalizable without imposing any projectability condition.