  We consider the diffeomorphism invariant gravity coupled with the ideal fluid
in the non-standard 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 non-standard 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 FRW cosmology in same cases may be
different from the one in General Relativity with the possible
quintessence/phantom-like inflationary stage.
