Delsate, Terence and Steinhoff, Jan (2012), "New Insights on the Matter-Gravity Coupling Paradigm", PHYSICAL REVIEW LETTERS, 109, 2.
Abstract: 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 Banados 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.