A proposal for covariant renormalizable field theory of gravity

TL;DR

This paper proposes a covariant gravity theory with improved ultraviolet behavior that appears renormalizable, involving Lorentz invariance breaking due to scalar field coupling, and explores cosmological solutions and extensions to more complex models.

Contribution

It introduces a covariant, potentially renormalizable gravity framework with Lorentz invariance breaking via scalar fields, and extends to modified gravity models with Riemann and Ricci tensors.

Findings

Covariant gravity theories with good UV behavior are proposed.

Accelerating solutions are found in cosmological models.

Extensions to more complex modified gravity are constructed.

Abstract

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.