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A covariant scheme for matter coupling with a GL(3,R) gauge formulation ofgravity is studied. We revisit a known Yang-Mills type construction, wherequadratical power of cosmological constant have to be considered in consistencewith vacuum Einstein's gravity. Then, matter coupling with gravity isintroduced and some constraints on fields and background appear. Finally weelucidate that introduction of auxiliary fields decreases the number of theseconstraints.Comment: 8 pages, LaTe

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