On Consistence of Material Coupling in a GL(3,R) Gauge Formulation of Gravity

TL;DR

This paper investigates a covariant approach to coupling matter with a $GL(3,R)$ gauge formulation of gravity, highlighting how auxiliary fields can reduce constraints and improve consistency.

Contribution

It introduces a covariant scheme for matter coupling in $GL(3,R)$ gravity and shows that auxiliary fields help decrease constraints, advancing gauge gravity formulations.

Findings

Auxiliary fields reduce the number of constraints in matter coupling.

A covariant scheme for matter coupling in $GL(3,R)$ gravity is developed.

Quadratic cosmological constant terms are consistent with vacuum Einstein gravity.

Abstract

A covariant scheme for material coupling with $GL(N,R)$ gauge formulation of gravity is studied. We revisit a known idea of a Yang-Mills type construction, where quadratical power of cosmological constant have to be considered in consistence with vacuum Einstein's gravity. Then, matter coupling with gravity is introduced and some constraints on fields and background appear. Finally, exploring the N=3 case we elucidate that introduction of auxiliary fields decreases the number of these constraints.