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

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.