New Insights on the MatterGravity Coupling Paradigm
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 gravitymatter coupling. The Eddingtoninspired BornInfeld 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 singularityavoidance perspectives. We use these results to discuss the impact of changing the coupling paradigm.
 Publication:

Physical Review Letters
 Pub Date:
 July 2012
 DOI:
 10.1103/PhysRevLett.109.021101
 arXiv:
 arXiv:1201.4989
 Bibcode:
 2012PhRvL.109b1101D
 Keywords:

 04.50.h;
 04.20.Dw;
 98.80.Bp;
 Higherdimensional gravity and other theories of gravity;
 Singularities and cosmic censorship;
 Origin and formation of the Universe;
 General Relativity and Quantum Cosmology;
 Astrophysics  Solar and Stellar Astrophysics;
 High Energy Physics  Theory
 EPrint:
 6 pages, 2 figures, v2: revised version, v3: published version