Covariant renormalizable gravity and its FRW cosmology

We consider the diffeomorphism invariant gravity coupled with the ideal fluid in the nonstandard way. The Lorentz invariance of the graviton propagator in such a theory considered as perturbation over flat background turns out to be broken due to the nonstandard coupling with the ideal fluid. As a result the behavior of the propagator in the ultraviolet/infrared region indicates that some versions of such theory are (super-)renormalizable ones (with appearance of only physical transverse modes). The Friedmann-Robertson-Walker cosmology in some cases may be different from the one in general relativity with the possible power law inflationary stage.