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

We discuss some of the consequences of changing the matter to gravity coupling without affecting the gravitational dynamics. The Einstein tensor is usually assumed to be proportional to the stress tensor due to the divergence free property of both object. This is not the only consistent way to couple matter to gravity; we explore some aspect of consistent modification to the matter/gravity coupling using the recently proposed Eddington inspired Born Infeld extension of gravity.