Covariant Renormalizable Modified and Massive Gravity Theories on (Non) Commutative Tangent Lorentz Bundles

TL;DR

This paper develops covariant, renormalizable modified gravity theories on (non)commutative tangent Lorentz bundles, enabling exact solutions with off-diagonal metrics and addressing ultraviolet behavior, ghost freedom, and Lorentz invariance breaking.

Contribution

It introduces a framework for constructing exact solutions in modified gravity using nonholonomic frames and extends it to include covariant renormalizable models with noncommutative variables.

Findings

Exact off-diagonal solutions depending on all spacetime coordinates.

Models exhibit good ultraviolet behavior and potential ghost freedom.

Extension to covariant renormalizable theories with noncommutative variables.

Abstract

The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to nonholonomic frames with 2 (or 3) +2+2+... spacetime decompositions. This allows us to construct exact solutions with generic off--diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (un-) broken symmetry parameters. Such nonholonomic configurations/ models have a nice ultraviolet behavior and seem to be ghost free and (super) renormalizable in a sense of covariant and/or massive modifications of HL gravity. The apparent noncommutativity and breaking of Lorentz invariance by quantum effects can be encoded into fibers of noncommutative tangent Lorentz bundles for corresponding "partner" anisotropically induced theories. We show how the constructions can be extended to include conjectured covariant reonormalizable models with massive graviton fields and effective Einstein fields with (non)commutative variables.