Motion of a "small body" in non-metric gravity
  We describe "small bodies" in a non-metric gravity theory previously studied by this author. The main dynamical field of the theory is a certain triple of two-forms rather than the metric, with only the spacetime conformal structure, not metric, being canonically defined. The theory is obtained from general relativity (GR) in Plebanski formulation by adding to the action a certain potential. Importantly, the modification does not change the number of propagating degrees of freedom as compared to GR. We find that "small bodies" move along geodesics of a certain metric that is constructed with the help of a new potential function that appears in the matter sector. We then use the "small body" results to formulate a prescription for coupling the theory to general stress-energy tensor. In its final formulation the theory takes an entirely standard form, with matter propagating in a metric background and only the matter-gravity coupling and the gravitational dynamics being modified. This completes the construction of the theory and opens way to an analysis of its physical predictions. 
Kirill Krasnov