Mimetic Hořava gravity

We show that the scalar field of mimetic gravity could be used to construct diffeomorphism invariant models that reduce to Hořava gravity in the synchronous gauge. The gradient of the mimetic field provides a timelike unit vector field that allows to define a projection operator of four-dimensional tensors to three-dimensional spatial tensors. Conversely, it also enables us to write quantities invariant under space diffeomorphisms in fully covariant form without the need to introduce new propagating degrees of freedom.