A proposal for covariant renormalizable field theory of gravity

Understand

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.