Covariant Renormalizable Gravity Theories on (Non) Commutative Tangent Bundles

TL;DR

This paper explores covariant renormalizable gravity theories on (non)commutative tangent bundles, demonstrating their potential for ultraviolet behavior, decoupling properties, and off-diagonal solutions with broken Lorentz invariance.

Contribution

It introduces a framework for constructing covariant, renormalizable gravity models on noncommutative tangent bundles with off-diagonal solutions and decoupling properties.

Findings

Models exhibit nice ultraviolet behavior.

Decoupling property allows generic off-diagonal solutions.

Inclusion of noncommutative variables encodes Lorentz invariance breaking.

Abstract

The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime coordinates via generating and integration functions containing (un--)broken symmetry parameters. Some corresponding analogous models have a nice ultraviolet behavior and seem to be (super) renormalizable in a sense of covariant modifications of Ho\v{r}ava--Lifshits (HL) and ghost free gravity. The apparent noncommutativity and breaking of Lorentz invariance by quantum effects can be encoded into geometric objects and basic equations on noncommutative tangent Lorentz. The constructions can be extended to include conjectured covariant reonormalizable models with effective Einstein fields with (non)commutative variables.