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

TL;DR

This paper investigates matter coupling in a GL(3,R) gauge formulation of gravity, analyzing constraints and auxiliary fields to ensure consistency with Einstein's vacuum solutions.

Contribution

It introduces auxiliary fields into the gauge formulation, reducing constraints and improving the consistency of matter coupling with gravity.

Findings

Auxiliary fields decrease the number of constraints.

Quadratic cosmological constant terms are necessary for consistency.

Matter coupling constraints are clarified in the gauge framework.

Abstract

A covariant scheme for matter coupling with a GL(3,R) gauge formulation of gravity is studied. We revisit a known 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 we elucidate that introduction of auxiliary fields decreases the number of these constraints.