One avenue—certainly not the only one—is this:

1.  [**The absence of nondynamical background structures**]{} implies “general covariance” in the sense commonly used by physicists [@Anderson]: gravity should be described by diffeomorphism-invariant expressions involving only the metric and other dynamical fields. This is a new assumption: while Lorentz invariance restricts nondynamical objects, it does not eliminate them. A flat background metric, for instance, is allowed by Lorentz invariance, but permits Nordstr[ø]{}m’s conformally flat theory and Rosen’s bimetric theory (see[@Will]); a nondynamical volume element, also allowed by Lorentz invariance, permits unimodular gravity [@Unruh].

We must still address the possibility of additional dynamical fields. We can, of course, eliminate these by fiat—in a scalar-tensor theory, for instance, we can call the purely metric piece of the interaction “gravity” and relegate the scalar to the status of an extra “fifth force.” Alternatively, note that our kinematic assumptions led to a picture in which the response of matter to the gravitational field depended solely on the metric. We might ask that the reciprocal response of the gravitational field to matter also occur solely through the metric, with no added fields whose sole function is to mediate between the two (as in, for instance, TeVeS [@Bekenstein]). 