Remarks on and cosmological extensions of covariant renormalizable gravity

Covariant renormalizable gravity is a Hořava-like extension of general relativity, enjoying full diffeomorphism invariance. However, the price to pay in order to maintain both covariance and renormalizability is the presence of an unknown fluid, whose non-standard coupling dynamically breaks Lorentz invariance. In this brief work, we identify and explain the nature of this fluid, which we note describes the conformal mode of gravity, and arises naturally in frameworks such as that of mimetic gravity. Finally, we lay out extensions of the covariant Hořava-like model, which can serve as a guide for future model-building in this area.