New insights on the matter-gravity coupling paradigm

Back in October 1915, Albert Einstein published his revolutionary theory of gravity, General Relativity. His first version of the equations named after him were actually not compatible with local energy conservation. The second version was modified accordingly and claims that geometry is proportional to matter content. The fundamental geometric object is the so called metric, which prescribes how to measure length and time intervals. As John A. Wheeler said, 'Matter tells space how to curve, and space tells matter how to move.' This is the tenor of the Einstein equations. Furthermore, the metric itself is dynamical and contributes to the energy, warping the spacetime. This is encoded in the nonlinear nature of the geometrical part of the Einstein equations.

Although Einstein's equations successfully describe a lot of astrophysical or cosmological phenomena, it is worth noting that there is something missing in the theory. For instance, galactic rotation curves can be understood only by postulating the existence of some weakly interacting, nonvisible dark matter. The birth of the universe requires an inflationary period, which in turn requires new matter content. In fact, the most successfully tested sector of Einstein's theory is vacuum, as most experiments are performed outside of matter.

On another hand, it seems legitimate to wonder why an intrinsically nonlinear theory should couple linearly to the matter content. This should be valid in some regime but there is no reason to impose it. Modified theories of gravity usually propose to change the geometrical description, generally leading to strong experimental constraints. Instead, the coupling between matter and geometry is most often left unchanged. A modification of this coupling deserves a comprehensive analysis, which is the purpose of our letter 'New insights on the matter-gravity coupling paradigm.'

We were working on a particular alternative theory, namely the Eddington-inspired-Born-Infeld theory, when we realized that it can be interpreted as a standard General Relativity model, but with a modified coupling. This model was brought up to date in 2010 by Banados and Ferreira, who showed that in some situations singularity problems can be avoided. Using the reinterpretation of the model, we put forward the mechanism behind the singularity avoidance and explicitly show the effect of the coupling modification.

Even better, we provide a relation between how matter affects the geometry and how we perceive matter. Indeed, if the coupling to geometry changes, we must interpret measurements in a different way. Otherwise one is led to the (probably false) conclusion that spacetime is curved by a matter source different from the one directly seen... This sounds familiar? It should! Indeed, modified couplings are yet quite unexplored, experimentally viable, and might provide new perspectives to currently unanswered questions, e.g., mimic the new kinds of matter proposed in cosmology.

arXiv link