A link between ghost-free bimetric and Eddington-inspired Born-Infeld theory

We provide an auxiliary field formulation of the full ghost-free bimetric theory which avoids the explicit presence of a square-root matrix in the action. This description always allows for a branch of solutions where the auxiliary fields can be integrated out to give back the ghost-free theory. For certain parameter regions the two formulations are dynamically equivalent, but in the general case another branch of solutions also exists. We show that this second branch, with certain restrictions on the parameters of the theory, is dynamically equivalent to Eddington-inspired Born-Infeld gravity. This establishes a definite connection between two seemingly unrelated theories of modified gravity.