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We discuss some of the consequences of changing the matter to gravitycoupling without affecting the gravitational dynamics. The Einstein tensor isusually assumed to be proportional to the stress tensor due to the divergencefree property of both object. This is not the only consistent way to couplematter to gravity; we explore some aspect of consistent modification to thematter/gravity coupling using the recently proposed Eddington inspired BornInfeld extension of gravity.

Eddington inspired Born Infeld Theory: A new look to the matter-coupling paradigm