Equivalence Principle for Scalar Forces

The equivalence of inertial and gravitational masses is a defining feature of general relativity. Here, we clarify the status of the equivalence principle for interactions mediated by a universally coupled scalar, motivated partly by recent attempts to modify gravity at cosmological distances. Although a universal scalar-matter coupling is not mandatory, once postulated, it is stable against classical and quantum renormalizations in the matter sector. The coupling strength itself is subject to renormalization, of course. The scalar equivalence principle is violated only for objects for which either the graviton self-interaction or the scalar self-interaction is important—the first applies to black holes, while the second type of violation is avoided if the scalar is Galilean symmetric.

Figure 1

One-loop contributions to the quadratic effective action for $\psi$ (solid lines) in the presence of an external $\varphi$ (dashed lines).