New synthesis of matter and gravity: A nongravitating scalar field

We present a new manifestation of the nonlinearity of gravity-matter interactions. We show explicitly that there exists a nongravitating dynamical scalar field solution in Eddington-inspired Born-Infeld gravity. This kind of solution has not been found in previous literature based on general relativity or other modified gravity theories. The perturbation analysis shows that the solution is a late-time attractor if the scalar field rolls down the potential. This indicates that there are two weak-gravity regimes in the theory - one in the general relativity regime, and the other in the Eddington regime.