  The class of covariant gravity theories which have nice ultraviolet behavior
and seem to be (super)-renormalizable is proposed. The apparent breaking of
Lorentz invariance occurs due to the coupling with the effective fluid which is
induced by Lagrange multiplier constrained scalar field. Spatially-flat FRW
cosmology for such covariant field gravity may have accelerating solutions.
Renormalizable versions of more complicated modified gravity which depends on
Riemann and Ricci tensor squared may be constructed in the same way.
