New insights on the matter-gravity coupling paradigm.

The coupling between matter and gravity in general relativity is given by a proportionality relation between the stress tensor and the geometry. This is an oriented assumption driven by the fact that both the stress tensor and the Einstein tensor are divergenceless. However, general relativity is in essence a nonlinear theory, so there is no obvious reason why the coupling to matter should be linear. On another hand, modified theories of gravity usually affect the vacuum dynamics, yet keep the coupling to matter linear. In this Letter, we address the implications of consistent nonlinear gravity-matter coupling. The Eddington-inspired Born-Infeld theory recently introduced by Bañados and Ferreira provides an enlightening realization of such coupling modifications. We find that this theory coupled to a perfect fluid reduces to general relativity coupled to a nonlinearly modified perfect fluid, leading to an ambiguity between modified coupling and modified equation of state. We discuss observational consequences of this degeneracy and argue that such a completion of general relativity is viable from both an experimental and theoretical point of view through energy conditions, consistency, and singularity-avoidance perspectives. We use these results to discuss the impact of changing the coupling paradigm.